David Gross- Quantum Chromodynamics(Day 1)

so it's a great pleasure to be here as always in Singapore and I'd like to thank KK Lars and all the organizers for inviting me to this wonderful celebration it was 223 years ago that I gave a talk at a Yang's 70th birthday in Taipei and that was a great pleasure and I was delighted to accept this invitation to return and I hope to be here in 23 years for another celebration my talk today is about what I regard as the most beautiful of all yang-mills theory is non abelian gauge theories QCD and we are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non abelian local symmetry local gauge symmetries now called yang-mills theories through physics this is the introduction to that paper where it is pointed out that the usual principle of as a topic spin symmetry is not consistent with the concept of localized fields this sentence has drawn some attention over the years because of course in some sense it is consistent is just not satisfactory and the authors pointed out a more satisfactory notion of local gauge of local gauge symmetry which didn't require the fact that you have to rotate the whole universe at once something that smells an action at a distance now symmetry of course has been one of the main themes of 20th century science and especially one of the main themes of Professor Yang's research symmetries have played such an important role because although the laws of nature that we strive to discover and understand summarize the regularities of events which are independent of initial conditions symmetries organize the laws of nature themselves they summarize the regularities of the laws of nature and constrain them and are independent of specific dynamics symmetry principles provide a structure and a coherence to our understanding of nature to the laws of nature much as the laws of nature provide a structure and a coherence to the set of events we use to explore nature and test our ideas now we recognize at the very least two general sets of symmetries as we have discovered in nature global symmetries and local symmetries global symmetries which are the oldest to be recognized and used in physics are regularities of the laws of motion the laws of nature but are formulated in terms of physical events the application of a symmetry transformation yields a different physical situation but all observables are invariant under that transformation that's what we mean by asymmetry so we can rotate our laboratory globally and the results of all experiments will remain unchanged because the laws of nature are invariant under rotations it's rotationally invariant or rotational invariance so rotating the laws doesn't change the experiment and we don't have to note in our paper where and when and at which angle our laboratory was situated associated with such global symmetries our conservation laws for example in the case of rotational invariance the ensuing conservation law is that of the angular momentum local symmetries are a little more abstract perhaps a little more subtle local or gauge symmetries are formulated only in terms of the laws of nature themselves the application of the symmetry transformation merely changes our description of the same physical situation it does not lead to a different physical situation now local symmetries gauge symmetries first appeared unbeknownst to the inventors in Maxwell's electrodynamics Maxwell's electrodynamics is summarized here the electromagnetic field strength the electric and magnetic fields are defined in terms of a auxilary vector potential and the dynamical law is Maxwell's laws the divergence of this tensor is R is some external conserved current and the field strength of a is a Bianchi condition this is Maxwell's equations in modern form there was great debate in the latter part of the 19th century as to what the meaning of this victor auxilary vector potential was at all since it doesn't really enter into the equations of motion and is not an observable at least was not thought to be an observable in any sense and indeed the equations are invariant under a somehow the screen here is shrunk there's a lambda there yeah maybe you can change by a gradient of a local field lambda of X and under that transformation there are the equations are clearly invariant but there are no new charges now Emmy neather showed that once you have any continuous symmetry of your equations of motion or the Lagrangian that leads to those equations of motion there will be associated a conserved current so given a local symmetry like this where a new changes by the divergence of a field which depends on X there should be a current labeled by that field an infinite number of conserved charges and indeed there are following nethers prescription you can construct currents J mu which using the equations of motion are just the divergence of this quantity a different quantity for each function land of X an infinite number of conserved currents and supposedly an infinite number of conserved charges but if you actually construct the charges they are integrals of total divergence of the electric field times land of X and therefore for all but lambdas that approach a constant at infinity they vanish there are no new charges in quantum mechanics there are no new operators generating symmetries of your Hamiltonian or of your States in the hilbert space so the local symmetries are symmetries of the Lagrangian the action the equations of motion but they lead to no new transformations of the physical Hilbert space they lead to no new transformations of physical objects they are in a sense describing a redundancy in our description of the laws of nature gauge symmetry in a sense oops again the screen is much too short and it is cutting off my final message which is gauge symmetry equals redundancy therefore for many years indeed before quantum mechanics people asked is gauge symmetry a real symmetry is the vector potential a real object big nerve famously wrote is there some way does anybody know I had a patient getting shrinking large in the screen let me see if I can go on I'll read it to you this this gauge symmetry is of course an artificial one similar to that we could obtain by introducing into our equations the location of a ghost the equations must then be invariant with respect to changing the coordinates of the ghost one does not see in fact what good the introduction of the coordinate of the ghost does so that was vintners comments about local gauge symmetries as expressing some real feature of the underlying physics but it was of course Einstein who first realized that there was something and Mills later pointed out in the case of isotopic spin that there is something that smells wrong about insisting on global transformations in his case of space-time special relativity was based on global Lorentz invariants where you make a transformation from one inertial frame to another but you transform the all universe to a different inertial frame and his theory of general relativity was based on local reaper a motorisation of space-time transformations and which of course we are celebrating this year the hundredth anniversary of Einstein's equations which embodied that local diffeomorphism invariants and gave rise to general activity when quantum mechanics came about actually even around the same time viol introduced a what he called a gauge symmetry a local dilatation or scaling transformation of space-time in the hopes of giving a geometrical derivation of electricity and magnetism this of course didn't work there was a problem of an eye appearing it didn't exactly work but London shortly explained that you could give a a gauge interpretation of electromagnetism as a complex phase symmetry which was quite natural in quantum mechanics which introduced complex wave functions to describe charged particles and Yang and Mills that extended this gauge symmetry to non abelian gauge groups where and where even to write down the equations of motion in a local form you needed to introduce the gauge potential satisfying the non abelian gauge symmetry the fact that you need this redundant field and consequent local symmetry to to express the laws of physics in a local fashion actually goes all the way back to Maxwell who realized that in order to understand the local and nature of electromagnetism it was necessary to reduce the gage potential but then in quantum mechanics the in order to describe the Hamiltonian equations of motion of charged particles you also in a local fashion you need a gauge potential so this redundancy which is one way of looking at local gauge invariance is a necessary condition to try to to formulate the laws of physics in a local fashion but what are its implications it doesn't actually transform the laboratory it doesn't lead to new conservation laws it's a redundant way of describing local physics but yang told us importantly is that it dictates the nature of the interactions gauge symmetry produces no new conservation laws it does something even more important it tells you how to describe the interactions of particles and of course that's why it's the basis of the standard model which as we learned following those exciting years in the late 40s and by the middle of the 1970s are all described by gauge forces 3 in addition to einstein's local gauge theory of space-time we have the three sub nuclear forces one two three that govern the structure of atoms and of nuclei and of sub nuclei and just about everything and this is of course been realized with now in a way that has been tested with extraordinary precision seems to apply just about everything we observe and measured with the exception of one the force of nature which has recently been confirmed the higgs sector which unless you believe in supersymmetry does not laterally fit into the gauge story has to be added although in supersymmetric versions of the standard model is it can also be thought of as a consequence of gauge endurance one two three our label actually the rank of the gauge groups electromagnetism was an abelian gauge group gauge symmetry and Yangon Mills extended that to a non abelian case and they appear in the weak and strong interactions with not just the one electric charge of Maxwell but two in the case of the week and three charges in the case of the strong in directions now yang-mills theory appeared in nineteen fifty four or six six five six I think the paper was published in 1956 no 54 so why did it take so long for it to real to find its way into the standard model there were of course from the beginning problems the problems were evident to the authors of the famous paper and to its first critics and indeed as Laura's commented it was quite brave in the in the face of such obvious problems in to proceed with such a bold hypothesis the problems were manifold I'm not going to describe them all but in my opinion the main problems in trying to apply Hank Mills theory to the weak interactions were twofold one the gauge massan's the carriers of the force the analogs of the quanta of light the photon were massless charged massless if the underlying gauge symmetry was a local version of isotopic spin and obviously such massless long-range forces not been observed and it was evident to yang-mills and to their critics like poly that that given the symmetry that was the basis of the theory the massless miss was protected there was no way to easily get rid of it so nature which clearly didn't was none physical idea the other problem was that the symmetries that one imagined may key turning from global to local such as isotopic spin or any of the other flavor symmetries as we now call them were not exact symmetries and again it makes absolutely no sense to try to gauge symmetries that are broken and at that time there was little I understanding of the phenomena of broke broken spontaneously broken symmetries symmetries that are broken by the vacuum but not in the equations of motion and and in any case even if one looked at broken symmetries which are commonplace in physics they appear in crystals where which break the translational symmetry magnetism which breaks the rotational symmetry of the laws of nature superconductivity which breaks a local electromagnetic age invariants and as it will turn out the electric electro weak interactions it is not uncommon that the energy landscape of a many body or relativistic quantum mechanical theory for example has as its symmetric state an unstable state of higher energy than the many possible broken symmetry vacui but even when trying to apply the idea of breaking spontaneously as happens in crystals or magnets the symmetries that might the non-abelian symmetries like isotopic spended might be gauged one runs into the problem that for every broken global symmetry there exists these modes that were very with dispersion relations that are linear or what we would call relativistic quantum mechanics massless particles so any any attempts to apply being Mills theory to the weak interactions Granite's of these problems of massless gluons or if you try to break the symmetry massless Goldstone bosons and as we all know both problems were solved in the early 60s by brown glare and Higgs and this mechanism not only explains how you can gauge in a consistent fashion a broken symmetry but when you do so as was done incidentally of course even earlier in BCS theory for the spontaneous breaking of local abelian gauge theories you both produce a mass for the carriers of the force with W and Z in the case of the weak interactions as well as eliminate the Goldstone bosons and of course that simple perturbative mechanism has been now confirmed brilliantly at slat at the LHC two years over just about three years ago where the Higgs was discovered as hypothesized in the simplest standard model now in the case of the strong interactions of problems were perhaps even more severe since it wasn't evident at all what the charges what the what symmetry the non abelian gauge symmetry could act on originally again it was thought to be flavor symmetry but all attempts to use flavor symmetry as a basis for a gauge theory of the strong interactions were failed that carriers of the force would have been Roma's ons which were certainly not massless and so on and so on also in the case of the strong interactions one couldn't do much anyway since since they were strong one didn't know how to handle them there the charges which as we know today are coloured quarks and gluons were totally hidden it's not that the symmetry was broken symmetry is not broken the charges were confined for hidden and no matter how hard one smashed hadrons together one never produced a quarter so although there were it looked some extent like hadrons were made out of constituents fractionally charged half-integer horks which had even color assigned to them there was no evidence of quarks in nature from me the breakthrough and I think the historically the breakthrough in understanding the strong interactions came with deep inelastic scattering experiments at SLAC which discovered that the proton did look like it was made out of quarks not only made out of quarks but quarks that were freely moving around almost non interacting when viewed at very short distances at very short times the scaling so-called observed was only understandable if the quarks interacted very weakly and the cross-sections obeyed quark model some rules and many of us were convinced by this that this is indication that the proton is made out of quarks which raises another mystery how come these quarks which are bound together in protons are moving freely seen by these experiments this experiment was awarded the Nobel Prize for the discovery of quarks now there's a the this freely moving behavior of quarks inside the proton when viewed at short distances is rather strange and although by then we had learned enough about quantum field theory to understand that forces could look different at different scales of physics do two renormalization due to the physical effects that give rise to the renormalization of the charge all theories that had been studied like quantum electrodynamics so successful had the obvious phenomena of screening electric charges it is natural that if you have a a medium such as the vac the quantum mechanical vacuum and you put a charge in it the various dipoles that make up the vacuum will rearrange and screen the charge so that the electric force that an observer observes will be larger as you get closer and closer to the bare charge and weaker at large distances this is exactly the opposite of what seen at the slack experiment where the force that between the quarks decreases at short distances in fact this phenomena of quantum field theories or of many body systems in general above it so I mean quantum field theories is true just about of all theories and four dimensions which is why Lars said that few of them there are so few four-dimensional quantum field theories in fact the only ones that seem to make physical sense are asymptotically three theories and was the reason for landau in 1960 that says landau in 1962 reach the can clusion that QED is inconsistent if you try to look at the bear charge of QED it becomes infinite those infinities occur actually at a finite distance it's the land l paul and he concluded that the Hamiltonian method or actually local quantum electrodynamics is inconsistent and must be abandoned well what we discovered was that non abelian gauge theories yang-mills theories have the remarkable properties in fact unique among renormalizable theories in four dimensions of asymptotically approaching free field theory of having the opposite phenomena of becoming free field like non interacting at very short distances and that could explain the scaling seen it's lack and that's why we propose that they be used to construct a theory of the strong interactions which is indeed to C V now anti screening in QCD the opposite phenomena could have been guessed at from a simple physical argument namely thinking about the medium which is the quantum vacuum as a mm-hm in magnetic terms and noting that there are virtual gluons the Anglos theory are charged once you make the gauge symmetries and those did non abelian the carriers of the force they're gluons or the W and Z there are themselves charged as they noted the carriers of the in those field were charged vector bosons and they behave as paramagnets as permanent magnets and the vacuum is full of them and if you put in a test magnet it's enhanced by those virtual magnets leading to a increase of the force at large distances and a decrease at shorter distances exactly the opposite of QED that is the consequence that the strong force mediated by the chromodynamic non abelian gauge field set up between colored quarks color being the charge does not obey Coulomb's law as it would in the absence of the quantum mechanical vacuum but instead which would of course need to a finite ionization energy but instead in the complicated QCD vacuum with fluctuating fields the flux is squeezed to form flux tubes and that leads to an increasing force as you pull the particles apart and a decreasing force as you push them together both to asymptotic freedom and to what is called confinement the fact that you can never pull the quarks out of the nucleus so the problems disappeared once the color is identified as the charge asymptotic freedom explains why the clerks are a good perturbative description of hadrons at short distances and the strong force that ensues at large distances explains why they're permanently confined inside hydrants so the key dynamical property of non abelian gauge theories is this asymptotic freedom and it that dominates the structure of the strong interactions the verification of that by the way took years and years this is 89 16 years afterwards these are this is how the force is decreasing as you go to shorter distances in this direction and although there some indication of decrease I must say a straight line fits this data just as well but nowadays the standard model QCD the asymptotic freedom have been tested with exquisite exquisite for the precision now to use such a theory to explain hadrons to explain the proton the neutron that came as on the strange particle the lambda etc etc is not easy because the force gets stronger and stronger at large distances you have to control the vacuum and this is a more accurate calculation this picture of what the vacuum looks like as fluctuating chromodynamic fields as seen in lattice QCD which it remains so far the only tool for precise controllable first principle calculations of hydraulic properties and has been enormous ly successful reaching a new level of maturity due to Moore's law and to theoretical ingenuity and I recommend that you down here it says C talk by Michael Kreutz later in the conference but I did want to just point to a slide which shows a comparison of the light Hadron spectrum of QCD as calculated by lattice gauge Theory again you don't see here the names of all these particles the proton I think is one of them here these are particles seeing and baptists involving B mesons and so they're up here they're quite heavy these are the normal particles the Rho the K the lambda the proton we can now calculate the first principles and controllable errors through 1% or better the mass spectrum of all those particles that were being discovered when when Yang and when I were graduate students its enormous ly pleasing but I wanted to justify my title and explain why QCD is a perfect theory it has no infinities it has no adjustable parameters it has no new physics at short distances or large energies this is somewhat of an exaggeration but you'll have to forgive me so first of all it has no infinities infinities ultra-violet divergences plagued quantum field theory since its birth in the 1920s so much so that the inventors of quantum field theory vikner Dirac etc gave up on quantum field theory they expected that it was just wrong they needed some other revolution in order to make sense out of it so in that sense QCD is nice there are no infinities period QCD has no ultraviolet divergences at all the local they are coupling the chromodynamic charge of the quark vanishes that's a synthetic freedom the only infinities that ever appear when you do say perturbation theory in the way we learn with Fineman diagrams or simply due to the fact that you're expressing observed physical observables which always refer to some finite distance in terms of those that are defined the theory at zero distance in a local theory now if you divide a meter one meter by zero meters you obviously get infinity but that's not anywhere in the physics and if you take the best way we have and again it's the best way we have to explicitly calculate in QCD namely reduce the put the theory on a space on a spacetime lattice of lattice face in a reduce the answer to the partition function say to a thereby to a multi-dimensional integral but finite dimensional and the weight being of course the exponential of the yang-mills action divided by the coupling constant as the fine and the lattice spacing no infinite quantity appears here and then you define the theory as the limit as a goes to zero the number of integrals gets bigger and bigger of course in a finite volume letting G of a approach 0 as calculable by asymptotic freedom you get a finite answer that's what people doing lattice QCD used to calculate the masses of hadrons infinite quantities never appear there are simply no infinities second of all there are no adjustable parameters now that's a bit of an exaggeration because quarks of course have masses which have nothing to do with QCD so we can't calculate them but they don't play a big role in hydronic physics they're very the light quarks are very light heavy quarks are very heavy to a good approximation we can set the up and down and strange quarks to zero mass heavy quarks to infinite mass they decouple we get a very good approximation to the real world everything else that is calculable the theory has a zing and Mills pointed out their original paper no dimensional parameter the coupling that defines the strength of the theory defines how what the scale of lengths are because it varies with length so we need some parameter physical mass to define physics but having done that the coupling is fixed by that scale and so all mass ratios are calculated and if you ask what the origin of the proton mass is and I in public lectures two young students I love to point out that their mass which they have no idea where it comes from I explained to them that it's all confined energy and it's calculable in terms of the one mass scale you need to introduce the place they were the inge those coupling is one all mass ratios are then pure numbers which in principle up to quark mass Corrections could be calculated with arbitrary precision so that's the first time we've had a theory with no adjustable parameters and finally every theory we've ever had in physics has buried inside of it its limitation some place where it breaks down usually at shorter and shorter distances in QCD there's no new physics at short distances or arbitrarily high energies in fact to the contrary at high and higher in energies qcv becomes simpler perturbation theory more exact we can in fact control a divergent asymptotic expansion which is what perturbation theory and quantum field theory is by going to shorter and shorter distances this has important conceptual and implications it allows us to extrapolate theoretically of the standard model to arbitrary high energies and it innocence solves one of Derek's famous large number of problems is about ten to the minus nineteen a very small number Dirac worried about but we can extrapolate the strong force gets weaker to a point where it joins with the other forces and this is one of the reasons that and the fact that gravity becomes strong at about the same Planckian distance is one of the strongest clues to how to unify the standard model forces with gravity and might explain why this number is so small it is simply that at the unification scale the nuclear coupling is whatever it is like one over twenty five something like the electromagnetic coupling at that scale and then as you go to larger distances you get to a distance where the force between the quarks is strong enough to hold them together that defines the size of the proton and thereby the mass of the proton which is all this kinetic energy in that confined space so you can calculate the mass of the proton compared to the mass of the cutoff or the Planck mass and it's the exponential of one over the coupling at this scale which for standard model like couplings is exactly the right order of magnitude so QCD is perfect because it's the first example of a complete theory if you ignore everything else in the world with no adjustable parameters no indication within the theory of a distance scale where it might break down as infinite bandwidth but of course in the real world we'd like to understand why su3 gauge symmetry what about the quarks why are they there their masses and that we know of course experimentally that there are other forces in nature including gravity so in the many years since QCD came completed the standard model there have been extraordinary impressive pests of quantum chromodynamics impressive calculations in quantum chromodynamics here are some of the ones I like which have to do with the running of the coupling has now been carried out to to many many loop order and and but again here I have on my slide see talk by George Thurman will talk about the application of perturbative qcd to LHC physics right true something like which is absolutely essential so in the LHC we now are look for new physics and typically one new interesting event per billion boring events but to pick out one out of one billion events you have to understand those 1 billion events with with enormous accuracy and the technology of calculating with in QCD the perturbative expansion is just totally amazing as well as the agreement with experiment which i showed here this is I think a guy jet calculation and experiment from CMS and note that this is 10 to the 11 and this goes down here at 10 to the minus one this is a factor of a trillion million million twelve orders of magnitude agreement of theory and experiment then of course there's the fact that quantum chromodynamics the theory of quarks and gluons can exist in different phases that we never dreamed of and which are being explored a trick and a palace at the LHC not just the Hadron gas of confined quarks and gluons that we see at low temperature and low chemical potential or low density but a quark-gluon plasma whose properties are being explored at Rick and at LHC and perhaps fascinating new phases that might play a role and neutron stars or quark stars or high-density nuclear matter but perhaps the most interesting new aspect that has been revealed of of non abelian gauge theories and especially 2-cd in the last 30 years has been its connection to string theory so when you pull quarks apart they form a because of the properties of the vacuum the flux is squeezed into tubes and mesons look somewhat like fat strings and this is why string theory emerged from an attempt to understand the nuclear force and the properties of hadrons the focus originally indeed was on open strings relativistic open strings with labels Qian Payton labels I think Qian is here with which the would describe open strings or engage their engagements where these would be the charges or labels of a gauge boson in the adjoint representation of su in [Music] indeed this connection between gauge theory and string theory is now gone from wild hypotheses that led to string theory now to something that everyone knows some special cases is true and is generally believed to be the case what is truly exciting however is that string theory discovered in its evolution that when you have to have open strings you can close them and that closed strings describe gravity and therefore string theory led to a a unification in its conceptual level between gauge theories theories of open strings with fundamental quarks or labels at their ends the closed strings that have no labels and describe fluctuations of the vacuum or indeed of space and time by now that has that understanding has grown and proven so fruitful that I think of the framework of theoretical physics in the following way not as quantum field theory the basis of the standard model and this bizarre theory of extended objects called string theory neither of these are theories by the way they're frameworks as being one on the same thing and we have many indications that this is the case some special cases where it is beyond question and this is the general framework in which exploratory research and theoretical fundamental physics goes on nowadays almost exclusively with a hope eventually of understanding how this eventually fits in or is picked out the beginning this began with what's called large end QCD what happens to yang-mills theory when you take the n1 of the rank of the gauge group to infinity and the remarkable thing is that there's an incredible simplification in that limit if you regard the number of colors not as three but as infinite or large you can show that the theory must be non interacting with an infinite number of stable glueballs so pure yang-mills theory is made out of glue balls in a confining theory the gluons are confined when n goes to infinity there is an infinite spectrum of massive glue balls but non-interacting all stable in fact you have an effective theory of in which as NC goes to infinity you get the classical limit and all quantum Corrections are governed by powers of 1 over N so large n end being the end of su n say for yang-mills Theory large n is like a something of a classical limit of PCP as well as a string theory that classical limit would be 8 could be described by a classical string theory classical theory has an infinite number of spectrum all the oscillations of the string clen classically it's non interacting there are no loops there's a lot of evidence for that in quite generality from the planar structure of Lyman diagrams in non abelian gauge theories in large n the fact that one of our and see 1 over 3 in fact tends to be a good approximation for ad Roenick phenomenology but most importantly we in string theory to this duality or mapping of string theory to gauge theory in fact since Lars is going to talk about the maximally super symmetric gauge theory I want to say a word about it I regard it as the hydrogen atom of quantum field theory what I mean by the hydrogen atom is an integrable model which is a good approximation to the real world and such integrable models that are good approximations to the real world have had an enormous impact in on physics over the years in fact they've guided the historical development of modern physics for example the simplest example of an integral role model that's a good approximation to the real world is the Earth's orbit around the Sun which is governed the good approximation just as a two-body force law which is 1 over R squared now one of our squared and 4 dimensions is nice because it's actually integral and this neglecting the other planets is a good approximation to the real world and it is lucky that it is the case because they would have taken Newton or somebody else Oh much longer to discover classical mechanics and Newton's law of gravitation if we weren't to have very good approximation living on an integral orbit this same picture played it absolutely important role in the early development of quantum mechanics where the Bohr model which has essentially assumes simple orbits with a 1 over R squared force law is such a good approximation to hydrogen atom because hydrogen atom is integrable and the Bohr law was a semi-classical quantization of a quantum theory which didn't exist so if one hadn't had before one's eyes this simple integral model it would have been very difficult for or to have guessed the semi-classical approximation to something that didn't exist yeah it led to nonrelativistic quantum mechanics the Dirac equation is also integral and that helped enormous Lee in the development of relativistic quantum mechanics so historically through relativistic quantum mechanics starting with integral models that are a very good approximation to the real world and then exploring the corrections is what led through classical mechanics nonrelativistic quantum mechanics relativistic quantum field do well asymptotically free QCD or non abelian gauge theory to some extent already is like that and that's why it's been so successful and possible to develop because again for very large momenta because of asymptotic freedom we have an trivially integral system of free not interacting quartz and gluons about which we can perturb and we which becomes a better and better approximation to the real world as you go to higher and higher energies but the most interesting one of this is maximally some up grote so N equals four is a maximal number of super symmetric extensions of yang-mills theory and again when the number of colors becomes infinite that theory becomes we believe in terrible we're very close to actually writing down the exact analytic on paper solution of this limit of of non abelian gauge theories or of QCD now if we wanted to make contact with QCD we would of course have to break su super symmetric supersymmetry not difficult put in quarks not difficult but calculations then become difficult as you perturb away from the integral limit but this in a way is the best exposés thing to the hydrogen atom and relativistic quantum field theory that we've ever had and it is amazingly informative and this is this understanding has partly been based on and feeds into this remarkable duality between gauge theory the one hand and string theory living in idea this is a BS CFD this theory this integral model is dual to a string theory in ten dimensions the limit of n going to infinity is the limit in the string theory of Planck's constant going to zero becomes the classical limit of that super string theory and here it says C talk by lars bridge so a word to get I think I'm going to skip this slide and trying to explain what a DLC of T is but just tell you how enormous lis productive this hydrogen animals and this duality between string theory and gauge theory it has given us new insights of course into gauge theory it produces a string theory of this cousin of QCD it allows us to tackle problems in QCD like say the transport coefficients of the quark-gluon fluid produced a trick before it decays into hadrons something which is beyond our capability directly in QCD but easy to calculate in string theory by solving Einstein's equations with surprising success the same applies to condensed matter physics the hallmark of this limit is hydrogen atom of gage theory this supersymmetric gauge theory is that it is conformally invariant it's conformally invariant it's integrable it's everything at once but the duality is more general any we now believe that any critical point any conformally invariant quantum field theory is dual has a geometric dual which is a stringy theory and in the certain limits can be described by the low energy limit of string theory which is einstein's there so you have now convinced matter physics solving Einstein's equations in order to learn about quantum critical points critical points that occur at zero temperature as you raise some physical parameter again with remarkable insights these are insights between simplified models between hydrogen atoms okay but they are what is one of the reasons as Michael Fisher I'm sure will tell you that one studies simple systems to learn about the qualitative nature of very difficult physical phenomena like one on critical points from the point of view of fundamental physics most importantly this gives us new tools now starting with a gauge theory which is a know by now a standard quantum field theory we can put on a computer and calculate two questions about quantum gravity which are string theory is ethereal and is being used to try to resolve some of the puzzles of quantum gravity like the fate of black holes and the nature of quantum cosmology and down here I have new concepts of space and time so I'm going to end by coming back to my original point about local gauge symmetry redundancy what is the deep meaning of this gauge symmetry that you Mills generalized from abelian to non-abelian is it just a redundant description of physical phenomena well in this new world of string theory field theory correspondents this becomes a more even a more interesting question in string theory in the string theory you do don't see the gauge degrees of freedom at all when you to make the correspondence you can associate those gauge degrees of freedom as dynamical modes of brains might be sheets or three-dimensional volumes points where open strings end that's where the gauge charges lay so in string theory to construct gauge particles you have to you put in collective vibrations of string theory of space-time if you want which are say sheets open strings can end on those sheets and those strings that connect them are the gauge connections and the places where they end where they gauge charges are so in a sense from the string theory you can construct these redundant gauge degrees of freedom if you want but they're clearly redundant and not visible directly in the gate in the string theory conversely in gauge Theory you can regard space-time itself of the corresponding string description and dynamical space-time otherwise called gravity as descriptions of the dynamics of the gauge field and dozens of theorists are now engaged in making a precise understanding of how space-time emerges or could be constructed out of the dynamics of a gauge theory on a rigid four dimensional space so this makes the question of what is this redundant description of physics or gauge symmetries gauge degrees of freedom more interesting our gauge degrees of freedom emergent from modes of dynamical space-time or is space-time emerging from gauge dynamics or both so I'm going to leave you with that question it is at the center of what we are doing nowadays at the frontiers of fundamental physics how it will help us answer the question of where the how does our standard model fit into this much wider and richer framework we've studied I don't know but one thing I'm absolutely sure of that yang-mills gauge Theory will be at the forefront of fundamental physics their centuries to come thank you [Applause] [Music] let me before we start asking questions let me just tell it the story about what happened in 2004 when we called David to tell him that you had got a certain price and then this was two o'clock in bye Danny how well he can tell himself whatever but then we had the press conference afterwards and we had David on the phone so I was sitting there and had microphone next to me but that was David and so then one of the so they were you know hundreds of journalists from all over the world so the journalist asked him so when did you start to believe that your theory really was the correct one and David was very polite and he was yes he said well you know during the 80s when you know we saw the results come in and there you know they fit it so well then I started to believe in but then I clapped the microphone I said that's wrong I said you knew it one microsecond after I discovered it which I still think is true well there's knowing and knowing and yeah you know there there's the kind of noise so you could ask Frank when did you know that yang-mills theory was part of the real world now he might very you might very well answer the same thing for him immediately it's so beautiful it's so it must be part of the real world but then then there's the second knowing which is requires the agreement of the ultimate judge which is nature and that comes as always much much later so we're running late it has happened before when David talks but do we have any questions I think we if you don't have it now we take a coffee break and Moore's Law as you know is the fact that computers become twice as powerful every one 18 months that has helped lattice gauge Theory enormously lattice gauge Theory began in the middle 70s it was sort of as a tool for calculating hydrants was originated by Ken Wilson Ken gave up mic was one of the first to continue but they were working what by what is regarded today as extraordinary primitive computing and so at that you really needed modern computers to tackle this very difficult calculation ok as I said to all your young people feel free to ask David you know and he will be so glad to answer your questions outside here so I think we would take a break and we first have to take a group picture and then we have to take coffee and then we have to be back here by 11:00 so this is kind of we do it quickly

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Rating: 5 out of 5

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Id: sdj5ZN0_zoU

Length: 67min 20sec (4040 seconds)

Published: Mon Jan 29 2018