Where in the World are SUSY & WIMPS? - Nima Arkani-Hamed

okay so um the that's the official title of this lecture I'm going to give lectures on a number of different topics for my lecture so it's not going to be one coherent set of things but but what what I want to talk about today that's the official title and the the informal title is what the hell is going on and of course we we've had a number of lectures earlier in the school talking about the strange situation that we find ourselves in we've stressed many times that this was not a picture of the world that was popular or the majority of people would have predicted you know 20 years ago is definitely not the way things have turned out and and so there's a very natural reaction to that which has been advocating some of the lectures I've even advocated it as as something to do to think about go back think about all these things again from a totally different point of view maybe something completely radically 100 percent out of left field totally different than anything we've thought about before is going on and I could still be true what I want to talk about today is is something that has some radical crazy elements to it perhaps but is fundamentally at its heart more conservative and it's based on a certain kind of optimism that at least not just I have many many people have about our powers theoretical physicists that you know things work they tend to work they work more and more and it has not happened to us in a sort of very long time that a set of ideas that seem to be supported circumstantially or from internal theoretical structure other things just ended up being completely totally a hundred percent wrong you know they might have been misinterpreted you might have had to rotate your point of view about them a little bit but this idea that we gradually are more and more closely approached the truth while changing some of our fundamental assumptions as we go along the way something that's happened a number of times and so I want to tell you my answer to this question of where in the world they're Suzy and wimps and why haven't we seen them yet in that in that sphere right in other words there was a reason after all why people were so excited about these ideas 20 years ago 30 years ago and it wasn't just because it was a club of the cool kids who like supersymmetry and wimps there were things from data there was the spectacular success of the unification of gates couplings the very fact that they solved the hierarchy problem to begin with gates coupling unification slightly more qualitatively the WIMP picture of dark matter these are all things that fall into your lap without asking for them so so that was why people were excited and so that's our tension that's what we're going to deal with in this talk is how could those things have been true and yet where we in the situation we haven't seen any of them yet is there a picture of the world where every clue that we've seen in the last 30 years experimental clue theoretical clue about these questions mean something and that's what I want to talk about in this lecture and actually to put this in a broader context actually want to tell you what I think of as the really nearly 40 plus year history of this problem and I'm not just talking about the history for the for the fun of it but I want to I want to stress something which I think is not quite as widely appreciated especially in people in the in your generation which is that this funny situation that there is a set of theoretical ideas that seem to make incredible sense and the nature doesn't quite seem to agree with them this is not the first time it happened to us and in fact the very predecessor of the ideas that went on to become the supersymmetric picture of the world have that flavor to them already okay and supersymmetry was the fix to those little set of problems that ruled out the the previous series and in the story that I want to tell we're going to take the path of continuing this attitude to take the little problems that seem to be there in the previously great structure and taking them seriously and try to fix them and see where it leads us the picture we're going to be led to in the end the picture that if you put a gun to my head in the middle of the night and said what do I think is going on today and I wouldn't say it was a huge amount of confidence I guess you put a gun to my head so I would have to say something but the but the the apicture is something like the minimally split version of supersymmetry with a factor of parametrically a loop factor a numerically a factor of a hundred or a thousand splittings between the gay gino's and perhaps the higgs inos of a super symmetry and the scalars but anyway I'll try to I will tell you both the the reasons why that's what I would say if you put a gun to my head uh the the context of how we think about the inevitable fine-tuning associated with that theory the heresy of having something fine-tuned and super symmetric at the same time and also some theoretical opportunities experimental signals and stuff like that all right so indeed is the LHC shocking no I would say that from some point of view and I think if you took what we are learning from the data ultra seriously the whole time then there was a reason to be worried the whole time right from the start a chain of indirect argument stretching back for decades and so what I really want to do is start the story at the beginning and the end the hero of this first part of our story is going to be howard georgia with the grand unification okay now how many of you i was asking this question that's the breakfast earlier how many of you if I woke you up in the middle of the night and asked you ask you to just give me the quantum numbers of the standard model how many could you how many of you could do it you can be honest and not looking someone else polls I really mean like three two oh six three bar 1-2 Thursday bar 1 plus a third huh sorry well I didn't want to look in case people were embarrassed but how many people know it off the top of their head okay you should know it off the top of your head okay so uh I wasn't asking you not to you got it all right so okay okay so we have this crazy stuff right and um maybe we have some singlets as well as it might be right-handed neutrinos and I cannot imagine the feeling Howard must have had when he realized that these things when you realized that all of these things fit into a 5 bar plus 10 of SU 5 and then all of these things fit into a 16 of s oh 10 okay so you want this sort of clue from above that you're on the right track it's very hard to imagine a better clue from above that you're on the trike right track the map and as he likes to tell the story on the night he discovered all this he was drinking and I realized there was proton decay there had to be proton decay at the end and that made him depressed and so the next morning Ian Shelley realized that well if these if the new gauge bosons associated with the SU 5 we're very heavy if they're a 10 of the 14 GB 10 to 13 10 to 14 GeV the proton lifetime would be long enough right so a Tau proton is M got is M proton is I'm got to the fourth or M X Y to the fourth roughly over an proton to the fifth and so if you make this scale high enough you can make the proton a long-lived enough now right after that was the amazing realization that in fact not only could you group theoretically unify the interactions but if you took this the particle content and you ran the coupling constants up they in fact nearly met numerically okay so now today we know that these things the standard models are measured I'm just plotting alpha inverse here as a function of scale so so so today we know that they don't unify precisely in the standard model but just back up a second okay they don't unify precisely but they're still pretty close and uh they didn't have to come anywhere near each other a be the unification scale could have been at 10 to the 15 is logarithmic running right there's absolutely no reason that this mere coincidence has to happen at a scale let's call it 10 to the 14 to 16 GeV okay which happens to be close to the Planck scale too later the scale associated with right-handed neutrino masses or the seesaw two later we learn the scale associated with inflation if you want to do the simplest dumbest theories of inflation where you're not standing on your head the energy scale involved is the same scale none of this have to happen right we're not talking about it's a log scale it could have been off by by exponentially huge amount right and on top of everything else you know people other people work for decades and more complicated frameworks fancier frameworks and don't accomplish as much in 48 hours of their life as the hour did okay a it works being you get a prediction which you can immediately go tell your experimental friends to look for that you should see proton decay I can't imagine something more spectacular than that and of course the prediction is wrong right okay so that already is an example I think of a chain of theoretical arguments that are so tight they seem to have so much support circumstantially from nature all sorts of things work out and yet in detail they're wrong okay now what could this mean well you could take this as a slap on the wrist say you know even when you have amazing things going for you if they're circumstantial if you're not really up they're it's dangerous to speculate about what's going on at humongous energy skills right let's stay down at closer scales where we don't where at least we can check things is experimentally more more more quickly that's one attitude but I think it's useful to be bold whenever you can even if you end up being wrong okay you try to do something and and when you run into a failure you should ask whether the structure that you're had in your hand was already as perfect as it could be or if it had other nagging problems that should have bothered you anyway and if it did have other nagging problems that should have been bothering you anyway could it be that when you solve those problems though the nagging ones that these things that seem deadly will go away or get changed okay so in the context of this story so we've gone from the mid 70s to the sort of early 80s now in the context of this story what was the big nagging problem with this picture of grand unification anybody the hierarchy problem okay and in fact the hierarchy problem was in a sense first discovered by gut model builders I mean in this and the I mean it's discovered in many in many contexts within the one that sort of most relevant for particle physics it was first discovered by model builders even classically it was associated so there's a hierarchy problem is the elephant in the room elephant in room okay and ah and it originally showed up in the context of doublet triplet splitting problem and the difficulty is and I should have stressed here these are the fermions but of course we also have we also have the Higgs and of course the Higgs does not fill out complete a complete gulp a complete gut multiplet okay so it's a fermions like to fill out the complete got multiplet but the Higgs does not and so you might imagine if you had an su v gut let's say also imagine you have an f2 v gut there has to be a field sigma which breaks su v su 3 cross s to do growl c1 so the simplest thing to do would be to take something the adjoint representation of su 5 so a 5 by 5 permission traceless matrix and if the vehm of this matrix if the vehm of this matrix is m dot times 2 2 2 negative 3 negative 3 then that breaks su 5 down to su 3 cross su 2 cross you want by the way how many of you know this forwards and backwards I'm just curious how many people know about guts how this works forward and backward okay how many times am I gonna have to say this in this lecture not be actually I'll be curious when you don't put up your hands ah yeah so that so that so it's a small fraction of you know this forwards and backwards you should learn it forwards and backwards okay it's very beautiful standard important story anyway this verb breaks su 5 down to su 3 cross su 2 and then there's that u 1 generator that's also left unbroken and those two is and minus 3 is of the origin of all the funny hyper charges in the standard model okay just from some things coming out of the 5 bar plus 10 but now you have the problem where as the Higgs going to be and the simple thing to imagine is that the Higgs so so so a 5 bar contains the d conjugates and the elves okay so you can see that pretty easily that that precisely gives you the ratio of 2 to 1 for the hyper charges between the the d conjugates and the alt and so so work with the higgs be the higgs will have the quantum numbers of an L so you might think that the Higgs to is in a five or a five bar so we might imagine that we have a Higgs down here but then there's some triplet partner of the Higgs so this is our doublet with a sum triplet partner of the Higgs and we have not seen this guy we've only seen this guy so somehow when we break the gut we also have to give this triplet a huge mass while the doublet has got to stay like okay and how do you do that well the gut is broken so it's possible but what would I have to do would have to imagine there's a big mass squared for this huge for this four oh four for the five and then maybe there's a quartet coupling but the lambda H dagger Sigma squared H something like that okay and so after Sigma gets of EV after Sigma gets of EV the mass squared for the doublet the mass word for little H would be this like little M Squared you know minus 3 lambda m dot squared whereas the mass squared for the triplet would be little m squared plus 2 lambda M gut squared and so you see that if you very finely balanced lambda versus M squared it's possible to keep this light while you keep that heavy ok but that's what you have to do they're unified so this is the beginning it's not quite this still doesn't quite satisfy the requirements that we talked about and talking about the hierarchy problem of a theory that lets you really truly compute the weak scale from first principles because you still have this M squared parameter in the ultraviolet theory okay but still by by unifying it's it's going in that direction so it seems like in order to just do the simplest possible thing break the gut have a doublet light with a triplet heavy you have to make it crazy imagine a crazy conspiracy between parameters that have nothing to do with each other and that's how just a classical version of the hierarchy problem was born so there you go so there is an elephant in the room and so the the bolder attitude that you could have taken people did take of course is that it's not the general idea of unification that's wrong we've found a version that's almost right but there's something that's missing it has a hierarchy problem so what would happen if we try to solve the hierarchy problem to this picture okay so any questions about this so far now it's also historically true that just thinking about the hierarchy problem alone with no regard for unification by far the most spectacular a general possible idea that could solve the hierarchy problem would have been Technicolor so Technicolor is to my mind just theoretically is the most obviously beautiful and correct solution beautiful correct and deadly dead dead to death solution okay and really you know when you see this you're like ah duh right of course it's like QCD all over again we can get dimensional transmission it's awesome we more or less automatically get a customer that's due to symmetry everything is great um so what's the problem with this idea and now we come to the second hero of our story is the sava Sanaa palace of course the Technicolor goes back to Steve Weinberg then Lenny Susskind on this part of the story is uh just the electroweak symmetry breaking is spectacular but um but something immediately showed up with the Technicolor which is a difficulty with explaining again you want to explain more things not just you want to you have to explain more things we don't have an elementary scaler then you can't just port the physics that breaks the chiral symmetry is on the fermions of the standard model you can't just port that from an arbitrarily high energy scale if you don't have an elementary when we have elementary scalars we have you kal couplings that are dimensionless or there's you know classically marginal they run a little bit quantum mechanically if we don't have the Higgs there are no marginal operators we can write down and that means that you have to do something you have to generate flavor you have to generate the physics of flavor right around the same scales that you're breaking electroweak symmetry okay now again if from the perspective of someone who's getting intoxicated with the strongly coupled gauge theories and what they might do for you in the late nineteen seventies this is incredible because it means that you're going to you're looking for a theory that has to by its construction do everything it has to break the lecture weak symmetry and generate the fermion masses and all all the rest of it what a delicious opportunity but when you start trying to do it concretely you run into this sort of a big problem which is the problem that the Demopoulos and Susskind ran into when they try to explain the fermion masses and there's many versions of this of this what I want to say it quickly because it also introduces us very early on in the subject to the central tension of beyond the standard model building the difficulty with the EPC is that so so in Technicolor you imagine that there's some technique quartz TNT conjugate and that they get a condensate of order some lambda cubed which is of order roughly speaking the weak scale cubed so we're confirming on masses come from well the idea would be that there's an even larger group ah that could contain the Technicolor group where you could do it in more complicated ways but that's something that will have to link the standard model quarks let's say to the technique warts via these new gauge bosons and so the the second you have this you can square the operator you can have something like this on the other side maybe with T DS & T T conjugates it doesn't matter and from here so there are some new gauge boson its mass is something it's going to as well see it's going to have to have a higher mass than the than the scale then the the week scale well the point is that and now where does this come from well maybe it's dynamical symmetry breaking Turtles all the way up right so there's there's some other dynamics that gives rise to the breaking pattern of the large group down to the Technicolor group and then you have these XY like heavy gauge bosons associated with them but this coupling constant this gauge coupling constant in the ultraviolet breaks the chiral symmetries on the standard bottle okay because it involves a cork flavor here in a Tec the cork here and so therefore there's an opportunity for it to generate you call coupling and it does when we integrate out the a gauge bosons we get a mass in the end for our mass matrix mij that's schematically going to be of order this technique condensate so that's going to be a border v cubed over m ET c squared okay now already this is kind of cool because especially in the in the early eighties people hadn't even seen Z as top cork yet um out so we didn't know where it was and you see this lead you to expect that the fermions should be a little light right that the et si guys are heavier so this is even a nice mechanism that you might explain could could give you the Fermi on that hierarchy and perhaps even a sequence of ways that the groups uh broke could give you people called it tumbling could give you a series of different possible QCD scales and give you a more interesting picture of the hierarchies however now so one thing made this very problematic ten years later fifteen years later the top quark being heavy okay the top quark being heavy makes it a big problem because these et Cie gauge bosons the ones that are associated with the top have got to be very light so light they would mess up a lot of other things that's one one one problem but even before that even before that there's a there's a bigger qualitative problem that exactly the same thing could also give rise you could convince yourself if you have that you have to have these things give rise to for quark interactions now these for quark interactions so this will give us things again schematically that's like Q Bar 2 squared over m ET C squared okay so MATC has got to be bigger than the week scale right just in order to explain why the light quarks are light so this is not this is better this is more protected than being simply suppressed by the week scale right it's definitely more protected than that but parametrically it's actually of order and Fermi on squared roughly over a over V squared so what we'd normally call the you calles squared times a times Q Bar Q over V squared okay so if I just put in this formula for the masses right so now something you probably all know is that is that it's very bad to have higher dimension operators that violate flavor right at the weak scale right that's really deadly and we'll come back to that however Technicolor is better than that X and the technical is better than that they're not just suppressed by the weak scale they're suppressed to the extent that the firm young masses are like they're also suppressed they're just not suppressed enough okay it's a more detailed problem so in other words this theory even qualitatively would tell you yes this is a theory with light which a neutral currents should be small we generate hierarchies everything is fine they're just not small enough to agree with the real world okay and part of the reason is that if you're going to have higher dimension operators suppressed by the weak scale you really need some sort of near perfect alignment of these pre-factors with the breaking of the U 3 to the 5th symmetry Nate talked about associated with the standard model you Cal couplings and what we get here is a little too generic for that alright so so what do we learn from all of this so so so Technicolor's is beautiful it's also a tremendously conservative we've seen it that phenomenon many other places in nature it could have been right it could have solved the hierarchy problem it's a people said it had a lot of problems languaging neutral currents which is a numerical problem but even conceptually it would even predicted small flavor-changing neutral currents just not small enough okay so and so that's our first basic tension the first basic tension of beyond the standard model hierarchy problem model building is that on the one hand we imagine going up in energy scales of the mass scale that might suppress higher dimension operators if we assume there's the standard model and nothing else up to very high energies we get a beautiful understanding from the approximate symmetries of the standard model just from the fact that you don't have higher dimension operators the dimension fort couplings all preserve certain accidental symmetries the accidental symmetries explain why we haven't seen bearing on and lepton number violation okay okay we could violate bearing a lepton number but if the standard model is good up to let's say you know 10 to the 15 GeV then we don't have to worry and in fact maybe it's 10 to the 14 GeV and there's a dimension 5 operators for neutrino masses that even explains why the neutrino masses are where they are but there's some scale way up there these are so dramatic so dramatic that you say well maybe something taking care of them uh but there's all sorts of other little things right there's flavor violations that we just talked about there CP violations and these are things that go anywhere from 10 to Eevee to 10,000 to Eevee depending on the kind of process that you're talking about for example just to pick a simple thing I'm sure many of you are familiar with let's talk about the electric dipole moment of the electron okay so whatever this diagram might mean if there's some new particles that couple to electrons or to muons or anything let's talk about electrons then then and if they're CP violation which Washington there be in this model there's order one CP violation so we might expect those order 1 CP violation in the in the rest of the in in the rest of the theory well we're looking for an operator that looks like econ joget f mu nu e is after electroweak symmetry breaking some being I'm being a little sloppy but anyway we're looking for some operator like this or f du Lemieux if we're talking about the EDM uh this operator violates the chiral symmetry on the electron so we would expect that it's proportional to the mass of the electron and therefore just by dimensional analysis it's got to look like that over some mass scale squared massive heavy particles here and probably there's some weak coupling constants around so there's an alpha and that's the estimate you have for the electric dipole moment of the electron and if you put em at around 100 GeV you just get a number that's 100 times now a thousand times bigger than experimental bounce okay Taron just do it 10 to the minus 24 10 to the minus 25 centimeters okay now so that means that you have to that there's all kinds of things ah and only if we make this M much larger than these scales do we explain why we haven't seen any of these phenomenon so that's the beautiful success of the standard model there's the theoretical issue of the hierarchy problem that leads us to expect new physics here at the TV scale or even below okay so this is naturalness once new physics here and so that's that's the tension okay why if there's tons of stuff lying around above our head why haven't we seen it already indirectly especially when the most obvious reading would suggest that the next scale is quite a bit higher up okay now what was the attitude of people towards this very properly is that these are not problems these are not reason to throw this idea out again it's not a problem it's an opportunity okay because you're learning something about the structure of that physics that's going to solve the hierarchy problem you need to endow it with some structure some extra ingredients that explain why despite the fact that all the guys were lying around above your head all these effects were not there okay now let's keep going a little bit also partially related to these issues is there's another sort of qualitative fact which we see already here with BNL violation VNL violation or such a humongously big deal that you might just think that the underlying physics especially it's the weak scale somehow really cares is not breaking bearing on lepton number okay now the second you know that if you just assume that barring the lepton number are are good symmetries to the extent that we care about them ignoring exponentially tiny effects from the from the anomalies in the standard model and so on um then uh then there's the following obvious parity symmetry that Neal talked about already - one - the fermion number that's a good symmetry barrier number and lepton number okay so if we have baron number and lepton number of course we have firmly on number and so that is going to be a good symmetry of whatever your new physics is okay and now what's important about that and why do I put the Fermi on number in there because with this every particle on the standard model is neutral under the sky okay every standard model particle and the reason is that all the leptons and baryons that we have refer Miam okay so that's why when I add a Fermi on number there every particle in the standard model is neutral and so if the new physics if the new physics has any particle that's charged under the symmetry then the lightest of all those particles will be stable okay so this is the this is the explanation it's not specific to Susie or our parity or this or that this is why everyone on their dog who builds theories that solve the hierarchy problem or of new physics of the weak scale half the time you run into a natural Dark Matter candidate okay it's because it's not hard for this to happen all you need is to find some guy who's charged under it so for instance who is it in the m SS m and the m SS m it's the it's the it's the gay Gino's or the Higgs e knows because they don't have Baron and leptin number but they are formula okay or it could have been this neutrino because it's not a Fermi on but it does carry left on number for example okay so that means that that you should expect some reasonable fraction of the time the theories that solve that are going to solve the hierarchy probably going to give you some new stable particle at the weak scale and then all the arguments you heard about from Neil about wimps would tell you quite amazingly that's the the relic density for that guy is about right that didn't have to happen okay the the reason for having these has nothing to do with getting a Dark Matter to work out and yet Dark Matter works out okay now and of course this happens in the context of this happens in the context of supersymmetry as we just talked about so so in 81 the two heroes of our story so far the way I'm telling the story Demopolis and George I wrote an amazing paper how many of you have read the Demopolis George a paper all right you should really read this month with George a paper actually if you read it might get a little depressed because one paragraph of the paper is one research industry another paragraph is another research industry so it was a easy to do things like that back then but in this paper they proposed the basic picture of the MSM that we're that we know and love today of course there's many many other people talking about similar things at the same time but as model builders they gave us the framework that we're using today to try to make sense of a supersymmetric theories the idea of softly broken supersymmetry as the way to parameterize our ignorance of whatever the heck was breaking supersymmetry in the ultraviolet and then talking about what the consequences were how you have to deal with these tensions and opportunities for example how you have to make sure that that the that the scalar masses don't break flavor too much maybe they're universal for some reason so that you don't you don't screw up the flavor accidental symmetries of the assembly ball I have to deal with CP phases how you have stable neutral particles around so other people had noticed and so on and of course they also made a prediction for a gauge coupling unit before back then people talked about it in the language of predicting the Weinberg angle but but today we can think about it just as drawing this picture now that we know the coupling constants so well so here we have the Alpha 3 inverse alpha 2 inverse alpha 1 inverse okay and now we know that these things actually do unify to amazing precision percent level precision at 3 10 to the 16 GB at the time actually their prediction for sine squared theta was was further away from the data then then then the standard bottles so it actually looked worse than the standard model back then but as often happens with their experimental friends the experiments change the error bar is always within each other but by the end it's not true anymore and when these things were measured by lap finally is when this percent picture of precision gauge coupling unification came out and then we had Dark Matter as well again a little bit more qualitative but this is just spectacular okay I think there's no doubt that what's spectacular back then and it is still spectacular today okay so but so actually to me this is like the kind of circumstantial excitement of first seeing that that everything unifies into a five bar plus ten and a sixteen right it's another thing that sort of works it's maybe actually not as it may be an even and not as electrifying is that first one but but you take the first picture right everything is going great so if you see proton decay you don't see proton decay you come back you say there was a hierarchy problem you solve it right you solve it with the supersymmetry uh the coupling is now unified perfectly and it's such a high scale that you don't worry about proton decay anymore from XY gauge boson exchange that's fantastic too right so that little elephant in the room solving it was was worth it you both solve the problem you remove the obstacle to realize in the old dream and you got some other things that you weren't thinking about before right Dark Matter now now works so so now why haven't we seen this okay so what we're dealing with today is like been not seeing proton decay of 1984 why haven't we seen this why is this wrong or now we don't know for a fact that it's completely wrong from the LHC but what I want to spend the next few minutes telling you about is actually that to the extent that any of you might have this impression that everyone was convinced that this had to be right until at the until the LHC came along and didn't see it that's just really very far from the actual truth and there are many people I wouldn't say a majority of people but it was a sizable minority of people certainly including me but definitely not just me a pretty sizable minority of people who have been worried for a long time about the general picture so what I want to spend the next part of the talk talking about are the sort of back and forth the reasons why people were worried but what seemed to be the much stronger counter arguments to ignore the worries and what finally might resolve all the attention so so it is definitely not the case that it was obvious before the lhe that we should see supersymmetry because it was not clear that supersymmetry could not have shown up much earlier than the LHC okay and before I tell you anything more I tell you anything more detailed just think about it super naively this is a theory for to explain the W and the Z masses which are aware there are at 80 and 90 GeV right not at a thousand GeV so just even super naively it seems like the theory should give you a whole bunch of particles around 100 GeV right not ten times heavier than that and so that could have easily been accessible to to a left even left one but let me let me say this in a little bit more more detail the thing that today is often talked about as the fine-tuning problem of supersymmetry is normally people try to quantify it at some amount of tuning and you know I've learned the hard way that you should not spend any part of your life arguing about what is or isn't tuned oh the really important thing is that you know when it's not tuned you know when it's not tuned when you have some systematic expansion for some quantity there's a leading piece which is around the value that you want and the sub leading pieces are much smaller okay and if that works there's no tuning and no one is talking about it now if you're talking about whether a factor of 10 cancellation is good or bad or this and that you know we've already decided what kind of person you are and we're haggling over the price and and it's just not worth it okay and and we can invent measures and this and and you know you talk about Bayes theorem and I'll start killing myself completely pointless okay what's true is that we could have seen superpartners we could have seen slept on Sat 40 GeV okay we could have seen the stop at a 150 GeV and no one would be complaining now we would know that that was natural and now I want to explain why that was actually in slightly more detail that was a good expectation and something that you probably all know is that if you imagine I'm going to draw a picture of the RG ease for some soft math parameter in a supersymmetric theory as a function of scale that that the gauge interactions tend to make these things bigger just logarithmically but they tend to make them bigger okay so squarks if you start off at some math scale here with some M Squared just under the rge the mass squared gets bigger it gets bigger than slept on do so even if slept arms and sparks started comparable thus quarks will get heavier under the rge compared to the slept on okay same thing for the gauge inos the the ratio at one loop M over G squared is our G invariant so precisely the fact that the gauge coupling is getting strong means that the via via the egg AG knows the glue Eno's get heavier than the other guys so there's a general expectation then that the colored particles are heaviest it's not a theorem but I'm telling you why people thought this colored particles are heaviest okay so you would expect squarks gluey nose up here you'd expect leptons and electroweak Eno's down here we know you know you would expect the hierarchy like this okay but what about the Higgs where would you expect the Higgs to be on the one hand it's not strongly interacting but very importantly on the other hand it enjoys the biggest coupling there is of all in the theory which is the top you call a coupling okay and top Yukawa coupling pegs the soft mass of the Higgs to that of the stops and therefore to the color particles so the sort of expectation is that the Higgs soft mass gets pegged to the same place these guys are at okay now we can say that in a little bit more detail how many of you have seen these pictures you know maybe that's what the stop does but you see these pictures where you have a Higgs there and it runs negative right so you start with a positive mass squared just under the rge it runs a negative right okay now quick quiz should that scale be close to the weak scale what do you think so let's say I'm you know I've given you the theory up at the gut scale and Pig squared is plus 200 G V squared I run under the RG e and I discover that the scale that this cross is over is ten of the ten GeV is that good or bad how many people think it's bad how many people think it's fine nobody thinks it's fine well okay well all right well it's perfectly fine guys I'm sorry okay ah the scale where this cross over it happens means absolutely nothing and the reason is that the what is the RG doing for you the RG is summing the large logarithmic Corrections okay and what we're interested altom utley because there's an overall the overall scale of all the superpartners here is that is M is the hundreds of GV squared right I'm starting up the gut scale I just have to run run run run run run till I get to a scale that's comparable to what those masses actually are okay so it doesn't matter it doesn't matter where this crossover happens you keep running you keep running until parametrically you hit the scale that's of order M itself which would be hundreds of GeV and that's where you sort of stop the running and and understand what's going on there okay so so that's the picture that you would have that you would have expected indeed it's true that under the RG evolution the Higgs off mass parameter is driven negative that by itself doesn't explain anything of course who lives the mute term which can that can make it positive anyway but never mind that's the kind of picture you would expect that that because the top you can't coupling again this is all because this is all driven by by by lambda top Q H you see okay you would expect a picture like this and in a picture like that what would you expect the spectrum of the theory to look like the math squared of the Higgs is setting the electroweak scale so in this picture you would expect that the Z would be close to the top of the spectrum where the squirts and the gluey noes are in that neighborhood with the colored particles because the haze got dragged up there with them and thus leptons and electric Eno's would be lighter okay so now that's the reason this is the reason that if you look at the papers of my adviser and his friends from the late 80s and early 90s they were filled with super symmetric spectra with flop stands at 30 40 50 60 GeV okay um they weren't just it wasn't it wasn't because they were desperately trying to make a prediction for lap and it would be exciting if they saw something looks um it's because that's just what the theory does in the dumbest simplest way of running it and maybe there's a fancier ways of doing it but it was not a crazy expectation that left should have seen it okay the way I like to say this is that there was a natural expectation from theorists so let's contrast the natural expectation would have been a spectrum with the Z and thus quark and the glue a knows their and thus leptons and the Elector akeno's and so on here and then there is the actual nature Bowl which happens to not be natural with the Z and the Higgs down there and who the hell where the hell is everyone else okay so that's the real qualitative difficulty with the super simple you're in the qualitative difficulty with started to be seen already in the early 90s okay with left and it just got worse as we went up from left one to left to the late 90s in the early 2000s now what made it a little worse still is an even more detailed thing in in supersymmetric theories it's kind of a milder cousin of this problem but a model the cousin of this problem was the famous fact that it was hard to get the Higgs to be heavy enough to have escaped detection at left okay now you probably know that in in in supersymmetric theories in supersymmetry the higgs quartic coupling ultimately comes from D terms and so is pegged to G squared it's pegged to the G squared of s u2 and u1 and there's this famous fact that a tree-level the Higgs master really the Higgs kortek is bounded by MZ so it could have been lighter than MZ is because the quartic doesn't get bigger than G squared I can get smaller than G squared and so if the egg is going to be bigger than MZ you have to have some breaking of Susy you have to see some breaking of Susy and the dominant effect is that we're talking about the Higgs quartet coupling ultimately is what sets the higgs mass the dominant the dominant breaking is an RG e there's a logarithmic correction to the quartet coupling of the Higgs that just comes from a loop of tops okay again because lambda top is big so this is something of order I forget it's 3 or 6 but let's call it 3 lambda top to the fourth over 16 v squared log of what whatever the high energy scale is over over m Higgs ultimately okay and so what would happen is in a supersymmetric theories the court a coupling of the Higgs is set to G squared until you see supersymmetry breaking at the mass of the stop and then once you get to the effective theory beneath the stop you don't see the stop anymore and so the quarter coupling starts running like that okay the court a coupling starts running and so you get a correction to the court a coupling that's roughly this log M stop over m Higgs now the good news is if the sign is correct and it makes a Higgs Maps heavier didn't have to be good it made it lighter than we'd be more screwed okay it makes it heavier but you see what the problem is ah the problem is that to make it a little bit heavier you have to make the stops much heavier right for every factor of two that you gain here you're you're winning you're losing either the two squared in the tuning that you have to do because here because this is only growing logarithmically with the masses of the stopped all right now even to escape the left bounds which by the time left shut down was around 100 1415 GeV even to do that you needed this M stop to be about it to Evie okay and that's why when I was a you know postdoc every Susie conference there would be spectra of things to expect at the LHC and they were all what we would now call today horribly tuned terrible theories okay but with no apologies no comments nothing people would flash spectra with T V squarks TV Higgs II knows and you know if you're a meek person or I wasn't that weak but if you but if you complain it's it isn't let's define to in theory you know we're trying to explain the W and the Z at 80 90 GeV there say oh you're such a curmudgeon you know you're such a stick-in-the-mud who cares on the grand scale of the Planck scale and everything this is nothing these little percent whatever you care we don't care what I think just just a sociological statement what's hysterical is that the same people who did not care about these things back in 2000 or throwing the entire theory under the bus today and I think the other more I'll tell you at least my own reaction so far as what we've learned from the LHC so far up to this point is more or less confirming what we thought from the simplest possible picture of what was going on what's happening already in 2000 okay and I'll have the X 115 and now let's keep going a little bit I mean we can solve the RG for it but the scales aren't too far away if you just ask what do you have to do to this just this effect what do you have to do to push the Higgs up to 125 the answer is that the stop has got to be between ten and a thousand T V okay so you know no no screwing around just do the dumbest thing what is it telling us right what size of the log do we need where would it lead us to predict the reason there is such an uncertainty ten to a thousand is we don't know what the starting point is right we don't know if the original quarter coupling was all the way at the G squared or closer to zero and it's totally reasonable for it to be at either end if it was as big as G squared already you could tolerate which supersymmetry aficionados will call large tan beta which is putting it a bit of a large number into the theory by hand okay so you're putting in some factor of 50 in by hand to begin with then if you do that you can go all the way down to ten T V if ten betas of order 1 1 2 3 then the scales got to be 500 TV thousand TV ok that's just the fact so both of these reasons that so there's a sort of big reason that the qualitative spectrum looked wrong that's that's appreciated by people most forcefully articulated by people like Ricardo Barbieri already in the early 90s mid nineties late 90s and then this more detailed fact about it getting hard to get the Higgs mass heavy that that were already very good reasons to be to be worried there was something maybe only a little bit wrong but something something wrong with this basic framework all right let me pause there and ask if there are any questions up to this point now we're sort of almost caught up with the modern-day okay all right now what we're what we're people's attitude towards this well especially when we're talking about things that look like little dinky percenters accidents or tunings or whatever you want to call it I think a prevalent attitude which was perhaps perfectly correct might even still turn out to be perfectly correct is that you know this accidents happen you're freaking out too much it's not a big deal and you know accidents happen for example famously there all kinds of all kinds of little tunings that don't seem to have any deep explanation there's the fact that the moon almost perfectly eclipses the Sun that's a percentage tuning we'll talk a little about the landscape and anthropic reasoning but I don't see any I don't see any reason for for for that even anthropic reason for that tuning if anything there's a misanthropic reason because it was responsible for the depths of countless virgins in Central America a long time ago right Stephanie time these happen you have to sacrifice someone so to miss Virgie no traffic principal perhaps but there's nothing anthropic about it then there's all sorts of other little accidents if you go down to the next effective field theory down from us well actually just think about the history of particle physics how much of the history of particle physics was confused by total accidents you Cal won the Nobel Prize for the wrong particle okay the pion on the muon of a mass that's nearly identical to each other why no reason no deep reason as far as we can tell the charm of the Tau are nearly on top of each other that confuse people a lot about when that when the charm is first being being discovered is there are some nerves how could there possibly be even anthropic any kind of reason for that sometimes accidents happen and um if we go to the next effective field theory down from the weak scale we go to the scales of nuclear physics then there are some famous accidents in nuclear physics that most people don't talk about so much although through all this obsession with tuning and tropics that people talk about it more but I mentioned some of them in Nate's discussion or maybe one of the lectures earlier in the school but I'll just remind you again maybe I'll just give you the most the most striking one you know that Neutron or proton are bound but two neutrons are not bound okay now how much are two neutrons not bound by of course the way you measure how much something is not bound as you experiment Li measure the scattering length between nucleons okay the scattering length is proportional to the one over an energy denominator so the way people normally say it is that the scattering length is anomalously big for two nucleons but but that's like saying that the amount but they're not bound is around 100 ke V that's that's absurd when all the scales in this nuclear physics problem or 100 MeV that there's a one over a thousand the stuff coming out of the blue out of nowhere right now do nuclear physicists that they're obsessing about this I don't know too many nuclear physicists so maybe maybe they do it's certainly responsible for why nuclear physics is complicated because it's a tuned system okay it's it's it would have been easier if it was not as attuned but you know they have a lot of stuff to do a lot of data to explain a lot of interesting dynamics to try to worry about so they don't spend their time obsessing over these parameter accidents okay but there it is the next theory down seems to have something which has no has no deep explanation as far as we know these numbers like 1 over a thousand come up easily so this is an attitude that you could take that yeah maybe there are these hints of some percentage problem but maybe it's not a big deal accidents happen and and the LHC what's going to be sort of going to be pushing into the percentage level tuning region anyway stops at a TeV gluey nose at 2 2 and 1/2 TV and so on so that's you know if it was like that then we would see we would see everything anyway okay so what's going to happen now from where we are now to the end of you know till 2020 and then we'll get a little a little better or worse depending on your point of view the end of the high luminosity run that one will get into territory that was really forced to be worse than we had to even imagine back in 2000 2000 okay you know maybe it another factor of 10 more tuned again in a way that we shouldn't do except amongst friends but okay so these are all these little niggly detailed reasons to be worried about the picture of course now we'll switch to the more entertaining part of the lecture there was a big reason to be worried right the huge reason to be worried was that these naturalness arguments had the COS module constants sitting on top of them as a crushing weight and because exactly the same arguments as we've talked about number of times in the school exactly the same arguments that would lead you to make a prediction of new physics at the week scale for the hierarchy problem would lead you to predict new physics at the 10 to the minus 3 electron volt scale for the cosmological constant and so the CC is around 10 to the minus 3 electron volt to the 4th before 1998 we said it's smaller than that now we say it's that unless we want to call it dark energy and just up to scape things but if we call it what it is which is a cosmological constant as far as we can tell then then the CC is around 10 to the minus 3 electron volt to the 4th the length scale associated with that is a millimeter and we can all do the experiment in real time nope there's no new physics at the millimetre okay so it's wrong this so this basic philosophy is wrong now I want to point out something that supersymmetry could have solved the cosmological constant problem okay I imagine that you are some there's some hidden sector and there are creatures in that hidden sector whose atoms were I don't know a kilometer big okay so these creatures are really big they're huge big big creatures but they're out there they there they discover physics you know they notice that they're a small fraction of the universe so there's a dark stuff right but they also discover called marginal constant and the theorists in this other sector think and think and think what could possibly solve this problem and they say Oh supersymmetry could solve the problem supersymmetry at the millimeter scale right so they're big they're kilometres big so millimeter scale is some tiny their atoms are kilometres big so millimeter scale it's a miniscule thing for them so they have to build the large millimeter collider right they build the large millimeter collider or not now they could have solved the problem it's not there okay so in other words their disappointment at supersymmetry would begin with its failure to solve the cosmological constant problem okay we didn't expect it of that just because you know it's so manifestly does not okay but it could have solved this the CC problem and it did not okay so now so that's that's that's the problem everybody knew it okay so this is the even bigger elephant in the room with the hierarchy problem so I'll make an even bigger elephant in the room okay then before and what would people's attitude towards this people's attitude towards the cosmos the constant problem is its deep its deep boy you say it's deep and you say the words uv/ir enough and you you say yeah right it's really super deep okay let's see with gravity cosmology deep deep deep and something else solves it okay ah and and meanwhile maybe it's not related to the hierarchy problem okay so so this has to do some magic mystery mechanism so the the best idea for the cosmological constant is what I'll call the magic mystery mechanism which makes it zero okay for some deep deep deep deep reasons it makes it 0 okay that was people's attitudes of the TC so we should ignore it it's too hard a problem attitudes quantum gravity cosmology all sorts of other stuff meanwhile the the hierarchy problem is just a little problem and an accessible energy scale there's no reason all the drama of understanding of quantum mechanics and space-time and all that stuff should come in and we should just be able to solve this problem by the way once again it could be a perfectly correct attitude it might still be the right attitude might be the right way things are after all as Nate reminded you and is in his lectures we've seen things like the hierarchy problem before recently in the history of particle physics and you could have taken this like deep deep deep we don't know so just or you could have worried all the calls model constants the elephant of the room so let's not bother trying to understand the charge PI on neutral PI on mass difference I don't having a very bad idea because those things are explained in a perfectly rational normal simple ways or the mass of the charm you could have said all these divergent saying none of them make any sense we should because we don't understand the CC problem it would have been a bad idea right so that's the difficulty with the history especially in physics is that you can choose episodes from history to illustrate any polemical point you want to make and we never know at any time which lesson we should take it sometimes lessons that we haven't even learned before of course but anyway that was that was a big big problem um but I think most people's attitude with that as I said there's a magic mystery mechanism it'll be solved separately and meanwhile there will be a natural solution to the hierarchy problem despite all these niggling nagging worries about it that we just reviewed ok what am i doing but then of course came along Weinberg and as I said in my introductory remarks you should pay extra special attention to people who have been right about nature there are very very few of them and they have a knack for doing it so it's useful to listen to them and hardly anyone was listening to Weinberg when he said this in 1987 but Weinberg pointed out and he was trying to do it as a way of killing anthropic reasoning how many of you know the Weinberg argument inside out so I know how long to spend on it ok even awfully inside out how many people have heard the Weinberg argument empty universal okay fine I'll say it relatively I'll give an intermediate amount of time to the argument so Weinberg says the following thing let's imagine let's imagine what the universe would look like as I made the called module constant more natural okay so um and so let's say it was bigger of course you can complain immediately here that we could vary a million things and not just a cause module constant but there is after something after all something special about the VFC see the thing that were confused about that's the most obvious thing to do first anyway let's just make the COS module constant keep everything else in the universe fixed and make the cosmological constant bigger and just ask what the world would look like we're going to go quite a long way before the word anthropic makes an appearance okay we're just doing completely legitimate physics exercise right you matter but everything is fixed I just make the CC bigger okay and then something remarkable happens right when the value of the CC becomes a little bigger than what we now know to be 10 to 100 times a lambda that we've seen now our lambda okay so he didn't know the universe he didn't know there was a CC so that's how we got a prediction out of this okay now we know there is so we can imagine doing this exercise make lambda bigger make it more natural already when it just gets ten to a hundred times bigger which in on the mass scale means the fourth root of that so we're not doing very much okay something very dramatic happens which is you know where does all the structure in the universe come from we have some primordial density perturbations probably they come from inflation or something like that but it doesn't matter where they come from there's some small primordial density perturbation the density contrasts with a part in 100,000 in the temperature in different parts of the sky when the universe cools enough so that matter dominates the regions that are a little over dense start clumping under the under the attraction of gravity and they gradually clump more and more and more take some time for them to a clump so that there's a ball here and a void there and a ball there and and eventually baryons fall into those uh those gravitational wells cool make galaxies although all the rest of it okay but it's crucial for this it's crucial for this that there's time for this to happen and the universe is decelerating and slowing down and down and down okay now what happens what happens if you make the cosmic constant just ten 200 times bigger is that before the matter finally clumps to make the little you know it's ball that's separated from the next ball over and so on it's clumping then the cosmological constant picks up and starts accelerating the universe and it blows that structure apart again okay so so I mean if we made it if we made it just for simplicity make it a million times bigger then well even way before make it big enough even before moderation in quality in structure doesn't have a chance of form at all so at least it has to be small enough for matter to be able to dominate and then it can't be and then you know in in more detail you have to not make it so big as to blow the structure apart before it actually forms okay so that's a quite a striking thing if you keep everything fixed and you make the CC just ten or a hundred times bigger the universe would be empty all right so so we can imagine that we do this so in this direction the universe becomes empty now as I said we're going to go ways before talking about the before saying the a word but just out of curiosity we can imagine what happens if we do the same exercise with the other parameter that we don't understand okay you don't understand or where you're were we find the Higgs Maps quite a little mysterious so let's do the same thing with the Higgs mass squared and let's again ask what happens to the universe as the Higgs mass squared becomes more natural so let's let's say let's take in the direction that it's already negative and let's make it more negative okay now this was an argument that was made by Donohue and collaborators in the late 1990s so here's where it is now so let's talk in terms of the mm here's the viv of the IG's Bev us if the exam is just something like three times us something terrible something let's not do the we're terrible something very new happens as well the fact that we have interesting chemistry in our universe the fact that we have this beautiful complicated periodic table and not just hydrogen is a big accident um you know you all know that neutrons decay in fifteen minutes in outer space right so um so what what why do we have neutrons in their nuclei why don't one all the just decay right there's some binding energy right but ah what does a neutron decay two proton electron three notes right so so there's an accident there that the neutron proton mass splitting is comparable to nuclear binding energies they don't have to be they're controlled by totally different physics one of them is all about the 2-cd the other one is about electroweak symmetry breaking up and down quark masses right so imagine if you make the Higgs bad bigger and bigger already many dudes just make it a factor of three bigger it turns out that the neutron proton mass wedding becomes so large that it exceeds nuclear binding energies okay just three times bigger and then there's nothing other than hydrogen so the fact that our universe has things other than hydrogen is it's a qualitative fact certainly important for our existence but again we haven't said the a word yet okay here in this direction as we make things more natural in this direction there's no atoms no atoms like plural atoms okay we just have hydrogen immediately okay now these are just fact again we know enough about field theories and the standard model to see to know what the universe would look like if we did this and if we did that right and okay it's kind of amusing that it seems like if we change these parameters just a little bit the structure of the world around those changes in some super radical way okay now admittedly this is quite a bit less super radical than that all right this really seems like really tremendously different okay now um how would we think about this in a sort of a conventional point of view the the connectional point of view that I was referring to of there's something natural for the hierarchy problem a magic mystery mechanism for the cosmological constant problem right how would we think of this fact ah from that worldview well you would say that's that's amusing that's cool fun fact okay because in this point of view and ah in this point of view where you sort of imagine that there's a unique theory okay and it's kind of tested it's very tacit even in the way we talk about tuning problems but let me be very explicit about it you want to imagine there's really some theory that's calculating for you the higgs mass okay and maybe also the occult logical constant and whatever that final series there's actually a formula there's a formula lambda over N plunk to the fourth and it's some formula I mean it's a function you know it's just going to be math there that's a route to e gamma Zeta of 3/2 knows right okay so there's some formula like that and there's a formula for the Higgs mass squared over N funk squared that's G of root 2 e gamma Zeta of 3 and so on right so there are some these are just come out purely out of dimensionless numbers okay and and so if that's your picture of the world if some parameter is crazily bigger a small like let's say we go back to the Higgs mask where why are we happy with the dimensional transmutation is a possible solution it's just that it's very easy to imagine what such a function might look like right you say oh it could have been either - one over and then you put some few bigger small numbers in there 3 PI squared ok and that's that's what it ended up being right so ah in other words when you have a mechanism that doesn't much care it's not too sensitive to what the choices of the parameters are it makes it easier to imagine there's a unique formula like this for them okay you don't have to you don't have to assume that some incredible identity between all these dimensionless numbers needed to be satisfied for the four things to come out the way you want so uh so so if you've managed to find a mechanism to naturally solve however it is if you've come up with a theory that really predicts one value for the Higgs mass squared one value for the cosmological constant that will be spectacular truly spectacular if the value was right but that theory is just giving you these numbers out of pure dimensionless of mathematical things and if there isn't some mechanism that looks like dimensional transmutation or something like that it's very hard to imagine that such a formula exists okay in other words it makes it hard in a theory that has one vacuum if you like or where where the micro physics in the end uniquely predict the values of all these parameters it seems like the best possible strategy for discovering what that theory is is to find find find a mechanism that generates these large hierarchies and protects them in all the ways that we've been talking about ok and if that's what you get then the fact that if in your mind you move these parameters around you say well you could only move them around in your mind in the true theory you can't move them around right if they're all they're all predicted anyway and then the fact that when you do this exercise in your mind pretending you could move them you notice these sort of amusing facts is just cool just huh what do you know right it would also look very much I mean certainly would look to me if this happened but that that whoever vented these functions carried an enormous amount about me okay because out of these pure dimensionless numbers my existence becomes possible and is hardwired into the structure of the ultimate theory of everything right okay that's slightly ironic I want you to absorb that if you imagine there's one vacuum and no anthropic that are from this point of view are our importance in the world is as large as possible right you know we're we're inevitable absolutely inevitable hardwired into these fantastic formulas that produce make our existence possible out of pure dimensionless mathematical fact all right but and maybe I'll just say a few more things about this and then we can we can fail to lunch a a curve on this but oh yeah uh no um the reason I drew it like this is because I really wanted these lines to be here but yes no that there's no no and they're they're they're they're decoupled from each other yeah they're just a couple from each other yeah yeah okay now the character of the question changes a lot though if the underlying theory which might be unique if the underlying theory has a property that it doesn't just have one vacuum or one metastable possible vacuum but has many many of them and again we're going to go some distance before saying da words but often this part of the discussion is associated with string theory and the string landscape and so on but it's not necessary for our purposes here and actually to be concrete I just want to give you a toy model a toy landscape just because it's easier to talk about this and all the conceptual issues are essentially identical ok now many of you are model builders if I told you that I took the standard model and I added to it a single scalar field with a potential that looked like that how many of you would Creek probably not too many people would freak right you know I mean you do much worse I'm sorry to say that so you know I just have something like that ok I just had one one one real scalar now notice already the theory of the world it's unique right it's a standard model plus this ok I've given the whole Lagrangian ok now this theory does not have a unique vacuum right so we have to decide which one we really Vin there's there's two of them this is already a choice you have to make already have to wonder what the universe looks like wire and one and not the other and but somehow for no very good reason when the number is two people don't freak out ok now let's say I have n of these scalars I just put an index on here they're decoupled it doesn't really matter just imagine I've end a couple scalars and oh and these coefficients are also depend on I so I have minimum that looks like this I have another one that looks like that you know and they're all they're all little different from each other one after the other okay now let's say I say I have five of these scalars are you freaked out now how many vacu are there there's 32 evacuee there's two to the fifth vacuole right now there's 32 vacuole okay now I tell you I have 500 of these scalars say 500 scalars that's ridiculous how many fermions are there in the standard model quick quick quick 90 fermions in the standard model okay but we count Felicity's uh-uh you know okay 90 fermions 200 scalars big whoop right what's so much better about one than the others not like the standard ball the most pristine beautiful elegant little construction we've ever seen either right so okay let's say we have n of these scalars we have two to the n minima right and that's the only thing that's the only important thing is that getting getting an exponentially large number of vacuo is very easy okay now this is not quite the way the string landscape works but it's pretty close okay in string theory you talk about fluxes and compactive occasions fancy columbia pictures and all this stuff but in the end the four-dimensional effective theories there's just a lot of scalars okay and it's a little more interesting than this because each scalar doesn't just have two minima but but if you like for every flux that you can turn on there's an effective scalar description for it with sort of many minima which whose local minima corresponds to turning on larger and larger values of the flux you get these sort of staircases so instead of having like you know let's call it a thousand scalars with two minima each you can have 50 scalars with 50 minima each okay and that's the kind of roughly speaking the way the string landscape looks but it really doesn't matter for the purposes of this discussion what I want to stress is that the theory can be unique and complete this is it this could be the theory of everything maybe this UV completes it to string theory we're done right that could be that could be the whole the whole world ah but we wouldn't be done to describing who we are right how we find ourselves in here despite the fact that the theory is unique now there is actually something amusing about this particular model which is let's now ask how it couples to the standard model and at leading order if I imagine that all these scales are triggered parametrically smaller than the Planck scale okay at leading order what I have is couplings like you know by eyes that can couple to our Higgs Phi I squared that can couple to our Higgs and that's it those are the leading couplings those are the leading ways of this couples to the standard model these are the only relevant and marginal interactions that I can have between the Phi's and the standard models and everything else would be like you know Phi over m + FF dual F squared or whatever okay uh other things like that so let's ask in these two to the N vacuum what does it look like in each vacuum okay well the scale is in a different place right but what's happening to the standard model parameters well G squared for example one over G squared plus G squared is not changing much I'm summing over these this is some some of the Phi I with some coefficients but let's say the Phi's are a little smaller than than M Ponk right as you move around this is not varying very much so the coupling constants aren't changing new cowls aren't changing none of those things are changing what is changing a lot what's the first thing that's changing a lot even before a coupling to the standard model the vacuum energy is changing a lot right because there's two to the N different possible values of the vacuum energy but these two to the N values are somewhere between plus M plunk to the fourth or plus Capital m to the fourth minus Capital m to the fourth the scale associated with this potential so I can't get too big or too small sum between I guess I call the scales mu and M but there are some like m to the fourth the negative m to the fourth with some constant out in front probably but I have to to the end of them so I'm stashing a Brazilian of these guys in here right so that's the first thing that happens in these different vacua you have a you have a huge number of them but they're stacked in a fairly small range and the first thing that happens is that whether you like it or not it is possible to find a vacuum that has a tiny value for the cosmological constant okay just accidentally there is one that has a tiny value of the cosmological constant we have still not said the a-word right I think it's very important it's there is a vacuum where the CC is the board of 2 to the minus n times m to the fourth ok now already this is an accomplishment because uh what we're saying before is that if we wanted to imagine a unique theory that was producing the cosmological constant that since we haven't found any natural solutions to it that concretely means we have not found any any physics any functions that can that can without insane conspiracies give us the value that we want but now we have right now the model is simple I haven't put any bigger particularly bigger small things in it ok and put in you know a thousand scalars right but I'm not making any conspiratorial choices between the coupling constants or anything like that the fact that you have an exponentially large number of metastable vacuous simply makes it possible to find one uh where the Kosmos constant is small of course there's many many other ones many more of them were as bigger but at least the first part is it even possible for it to happen this is making it possible for it to happen in fact it's only in the context of a situation like this where we have an underlying model and some sense of all what all the different possibilities are that in a sense the old-fashioned notion of naturalness can really make precise sense because now you want to imagine varying what the couplings look like if really in the back of your mind you thought there's a unique theory that didn't really make sense ok it was just kind of a guide or a guess for what you should be looking for whereas here it does make sense because they're all these other vacuo there or the couplings change and and so so so it makes it more meaningful to start asking questions about why you're in this vacuum versus the other vacuum this valley is a couple you versus the other valid coupling because there's at least a framework in which they're all there and which you can at least begin to try to ask questions about why you have this value versus the other one because the huge set of possibilities is at least allowed and there's so many of them that a continuum approximation is probably a pretty good one for for at least thinking about the distribution of possible values that you get for these couplings in the different vacuum okay so the first thing that changes is that it becomes possible to find a vacuum with a small t see what else changes higgs mass squared right he's not square it changes from vacuum to vacuum so so that's a cute little thing about this toy model is that this is actually a model that the legitimizes Weinberg's argument if you like or or not what but that that that I shouldn't say it like that definitely shouldn't say like that it's something that that is is correlated with the little plot we have that's hidden up there right because in this landscape the only thing that's changed a lot are the cosmological constant and the Higgs mass and everything else is more or less constant okay and why is it well it's a flip side for why fine-tuning is a problem to begin with when you have relevant operators when you make a percent change in them in plunk units such a big ass change right whereas when you have marginal operators dimensionless offers a percent change in them it's just a percent size defect not a big deal okay so now let's finish just quickly the discussion of this toy landscape I'm going a factor of seven slower than I wanted to of course but let's just finish our discussion here the of this toy landscape by now just asking if you're if you now wanted to ask what does cosmology look like in this theory uh certainly it seems naively that in order to in order to talk about why we end up in one universe what one vacuum another that perhaps cosmological history has something to do with it well then you start asking the question you imagine you start in one of these vacua let's say you start one of them with a positive cosmological constant and then you run the story the story that probably many many of you have heard about inflation and eternal inflation this was after all Booth's original model of inflation that didn't work as a model of the last 60 folds of inflation in our in our in our universe but if you start up there or the positive calls module consonant you know the life times the exact you it could be exponentially long with no problem okay it's trivial to imagine there's a small coupling here so the all the lifetimes are exponentially long and therefore while you're sitting in this vacuum and in flat space if you ignore gravity everyone would eventually decay down to the lowest of all the energy states because of gravity that doesn't happen okay when if you have a positive vacuum energy the universe is accelerating around you you're living in approximately in de sitter space and then when you come all to another vacuum you produce a bubble you don't tunnel everywhere at the same time to the new vacuum you produce a little bubble of the other vacuum that that expands out the bubble walls expand out of the speed of light again if there was no expanding universe underneath you one bubble would form another bubble would form they would smash into each other and if you waited long enough they would all percolate and you'd be left in the lower vacuum but because the universe is inflating around you these bubbles will never hit each other or very rarely hit each other and so this process keeps going and going and going and it never ends you make this bubble you make that bubble and then if you happen in the bubble to have gone to a lower energy vacuum that solves the positive cosmological constant well you keep going and keep going and keep keep going okay so now do we know that that picture makes deep theoretical sense no we don't okay that's it's suspicious to talk about regions that are outside the horizon there's all kinds of conceptual problems difficult conceptual problems associated with it but nor should we be scaredy-cats as theoretical physicists either as as the Steve Weinberg is often remarked we much more frequently make mistakes not taking our theories seriously enough than by taking them too seriously and so its usual to just do the dumbest thing you just do the absolute dumbest thing with this picture and that's what comes out of it right what comes out of it is is a cosmology where every one of these vacua exists somewhere okay somewhere in space in this infinitely forever eternally inflating large space star okay we still have not said the word anthropic we haven't talked about measures we haven't talked about any of those things but but a second thing that you need is happening not only is it possible to find a vacuum which has our tiny value of the cosmological constant that's possible not only that but somewhere it will happen no matter where you start more or less somewhere that possibly will actually be realized it'll be realized an infinite number of times everything else will also be realized an infinite number of times but at least it becomes possible not only that it's there but there's a region in the universe where it's actually populated the final point and this is where the a word comes in is to say well what does the universe look like there right so you look you now imagine just in your theorists God's eye a view of this global space-time which again is something to be perhaps suspicious about at a deep level but certainly just following the equations you can imagine doing this okay you look around and say okay here in this region the cosmological constant has m got to the fourth oh there are zillions of vacua here okay there's this one there's that one I don't know how to compare how much more of one there is in the other that's this infamous measure problem but I don't care I'm looking at that one this one's empty okay am I going to live there am I surprised that I don't find myself there no so I look around okay here they call them all with constants a weak scale to the fourth empty okay I keep going I keep going and taut finally I get to this ridiculously these tiny a much smaller fraction of all the vacuo down there where it's just not empty there okay and now of that subclass is not empty I keep looking around I said oh it's it's empty what do I have what it's all right it's not empty anymore what do I have oh it's it's hydrogen it's all nebulas nebulas nebulas nebulas nebulas oh look there now in this little tiny window I have like all of a sudden a huge number of complicated elements and it's and it's interesting and all sorts of structure happens right so invariantly from the top down even even still without saying word anthropic the kind of most interesting region of this large of this large inflating space-time the one that has some structure and things in it that are not just giant nebulas of hydrogen gas are the ones where precisely these parameters look like they have apparently very small finely tuned sizes okay now uh and uh and if it actually makes sense to talk about this God's eye perspective which I'll say for the tenth time it's not obvious it makes sense okay but the analogy people often give and it's not a great analogy but I will but but let's just say quickly the analogy people often give is here's a question about our universe we live on the planet Earth which is a tiny rock the volume of the earth divided by the volume of all of Hubble where we could live it's 10 to the minus 60 isn't that a big tuning why don't we talk about that as a giant fine-tuning of theoretical physics right big problem we have to worry about why we live on a rock well where else are we going to live right we're not going to live in outer space for one thing we're not going to live in the middle of nothing and we're also probably going to live in some giant gas nebula where there's a you know there's it's only some very boring elements and nothing else in other words if you're bothered for example if you say well I think I could just be made with hydrogen then I think it should be bothered that we don't live out there in giant gas nebula then you have a problem forget about those fancy stuff in our own universe you can wonder why we ended up on this little rock okay if it doesn't bother you in our universe that we were not in the void or not in the nebula then it should not bother you if you if you accept this idea that it makes sense to talk about the rest of this the vacuum of this multiverse okay to think it was some somehow real and and and wonder about why we're not why we're not there and we're here and so on in fact if it makes sense to ask that question and it makes sense to talk about them then the same kind of answer that satisfy you about why we live on a rock on earth should satisfy you about that okay the problem is it's not obvious that it makes sense and the huge difference and this is where there's a really huge difference is that the business about being on a rock on earth we can build telescopes and look out and say yep there's a void out there there's a nebula there if I look harder I can see other Earth's far away so I can confirm that this giant extra other space out there actually exists whereas we don't know even in principle even theoretically conceptually how to build the telescopes to see on the other side of our horizon whether all the stuff is actually out there okay so that's the huge underlying conceptual problem with this entire picture and that's why it might just be garbage for not philosophical polemic stupid reasons is it scientist and science most boring possible discussion but actually does it make sense does it make physics sense it's a physics question whether whether the picture makes sense or not it might not make sense but it might make sense we have we have examples where you might naively think it doesn't make sense to talk about things that are on the other side of a horizon but in the end everything all the information that's there are for example on the other side of the horizon or black holes we think eventually does make it out after the black hole radiates there's some sense in which some subtle correlations in the stuff that comes out of the black hole encodes of things that's that fell inside could it be in some way there's some subtle correlation in all the information in our universe that encodes the presence of all of these things outside maybe maybe not nobody knows but I'm just saying it's not a philosophy problem it's a physics problem and what it's certainly true is that in a model like this where well the starting point is not insane there is at least a new poss Oh picture for we're not just the cosmological constant but also the hierarchy problem could have an entirely different sort of explanation okay so I'm going to leave it there otherwise I will miss we'll miss lunch but what I want to take up tomorrow is you see this this was all known a Weinberg argument goes back to a 87 Donahue's argument is from the 90s even forget about the string landscape already Weinberg and Donahue were very strong reasons to wonder maybe something like this is going on so what so so why weren't why wasn't everybody worried about the hierarchy problem already then and a big part of it at least for me I can definitely for me but also I think from many of my friends and elders was that ok yeah the CC again is confusing but come on if the hierarchy problem is just crap if it's solved in this way that means it's a standard model nothing else up to the paunch scale then why were we seemingly on the right track with gauge coupling unification dark-matter unify mean all that stuff that whole historical trajectory that we talked about from 74 to the late nineties why did so many things that be seeming to be on the right track that was that's the attention now we have two kinds of tension we have the tension of putting all these things especially in supersymmetry at the weak scale gives us gauge coupling unification gives us dark matter there are some niggling things pointing us in the opposite direction there's the CC problem pointing in the opposite direction there's this kind of picture even making it perhaps possible that that the hierarchy problem could be addressed in a similar way so so but but between these two things the positive hints in the right direction from coupling constant unification and dark matter always overwhelmed the more kind of speculative more airy-fairy seeming arguments in the negative direction and so what I'll tell you about tomorrow is the the picture the only picture I know where all these hints are actually pointing in the same direction and that's the picture of minimally split I was planning on covering it all today so we could some totally different things tomorrow but well we'll finish talking about that in the first part of the lecture tomorrow and move on to different subjects all right thanks let's go to lunch [Applause]

Channel: Institute for Advanced Study

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Id: dKVXxcbJ4YY

Length: 100min 31sec (6031 seconds)

Published: Thu Jul 20 2017