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stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.
added (very) brief pointers to confinement in N=2 D=4 super Yang-Mills theory (in both these entries)
Very briefly cross-linked confinement and non-perturbative effect. Also added a pointer to (Espiru 94, section 7). (There are more canonical references for this of course, but I am on the road and a quick googling returned Espiru.)
Have expanded the list of references a little, with more on confinement via monopole condensation.
added pointer to today’s Simonov 18. Hm…
While confinement in plain Yang-Mills theory is still waiting for mathematical formalization and proof (see Jaffe-Witten), there is a variant of Yang-Mills theory with more symmetry where the phenomenon has been demonstrated
Is it possible that confinement only holds in situations with more symmetry?
Confinement is observed in nature, hence in Yang-Mills without supersymmetry: The fact that we consist of stable protons and neutrons, instead of being creatures made of waves in a quark-gluon plasma, is due to confinement. Confinement is also, apparently, seen in lattice QCD computer simulations.
So it’s clearly there in non-supersymmetric Yang-Mills theory, even though a clear idea for how to understand it conceptually or prove it systematically from basic QCD is missing.
But for supersymmetric Yang-Mills theory the theoretical situation changes, here one can at least give some plausible informal arguments for it (as pointed to in the entry). But to which extent a proof of confinement in SYM could be turned into one in plain YM again seems to be something that nobody has a good idea of.
A good moment to remind myself of the subtleties of what is meant by ’supersymmetry’, e.g., observed supersymmetryon the worldline.
But still, in that the Yang-Mills without supersymmetry of standard model can’t be the whole story, must it be that although wonderfully accurate about particle physics, it can account for all we observe? Couldn’t confinement act as a falsifier?
The key issue is that confinement is a non-perturbative phenomenon (due to the “assymptotic freedom” of QCD, which means that at the scales of the ordinary matter that our world is mostly made of, it is strongly coupled) and that the glaring open problem of modern physics is that there is almost no idea of how strongly coupled field theory works at all, away from toy examples.
Hence before one could talk about “falsifying” Yang-Mills theory in the non-perturbative regime, one would have to say first say what that theory is, in the first place.
Physicists like to say QCD is “non-perturbatively defined by lattice QCD simulations”, but this is, as so often, a means to sweep the real issues under the rug (nobody really knows how to take the limit of lattice spacing going to zero).
But one popular proposal for what might be going on is indeed a kind of completion of Yang-Mills theory in the non-perturbative regime, namely the suggestion that to complete Yang-Mills theory non-perturbatively one needs to specify/find/define its interacting vacuum, possibly the “instanton sea“-vacuum.
All this is wide, wide open. The Clay institute’s millenium problem “Mass gap in YM” is just one single aspect of non-perturbative QFT.
(In stark contrast to people going around and telling the journalists how fundamental physics is in such a crisis because we just can’t find anything that wouldn’t be explained by the standard model. This is really a weird thing to say: The standard model can’t even explain ordinary baryonic matter, due to confinement, and it can’t explain what’s going on with the most curious observation that the Higgs is pretty much exactly on the metastability line. )
The glaring open question of contemporary fundamental physics is non-perturbative effects in field theory.
(It’s not “quantum gravity”, not yet, anyway: Perturbative quantum gravity is well defined, already since 1973. While of course non-perturbative quantum gravity is a wide open problem, the same is actually true of every single non-toy field theory. So the real and first problem is to get any idea on non-perturbative physics at all. Of course, maybe non-perturbative physics can be explained only via recourse to gravity, such as in AdS/CFT.)
Fascinating. Thanks. I don’t think I’d seen that point made about what’s lacking in the standard model. Maybe we should add it somewhere to the nLab.
added pointer to
To the section “Possible realizations” I added a new subsection “Via Calorons” (here):
It has been argued that, after Wick rotation, confinement may be derived from the behaviour of instantons (Schaefer-Shuryak 96, section III D), or rather their positive temperature-incarnations as calorons, Greensite 11, section 8.5:
it is natural to wonder if confinement could be derived from some semiclassical treatment of Yang–Mills theory based on the instanton solutions of non-abelian gauge theories. The standard instantons, introduced by Belavin et al. (40), do not seem to work; their field strengths fall off too rapidly to produce the desired magnetic disorder in the vacuum.
In recent years, however, it has been realized that instanton solutions at finite temperature, known as calorons, might do the job. These caloron solutions were introduced independently by Kraan and van Baal (41, 42) and Lee and Lu (43) (KvBLL), and they have the remarkable property of containing monopole constituents which may, depending on the type of caloron, be widely separated.
$[...]$
The caloron idea is probably the most promising current version of monopole confinement in pure non-abelian gauge theories, but it is basically (in certain gauges) a superposition of monopoles with spherically symmetric abelian fields, and this leads to the same questions raised in connection with monopole Coulomb gases.
HI Urs,
this is a clear and illuminating quote from Krauss, if you want another one:
The second issue relates to the unobservable nature of quarks—again as central precept of the Standard Model, driven by observation. As Glashow suggests, the presumption that quarks are confined into color-neutral objects played a central role in the viability of the theory. But two aspects of this are worth providing a little more emphasis than was given in Glashow’s essay. While computer calculations strongly suggest confinement is a property of quantum chromodynamics (QCD), no first-principles proof of confinement yet exists for the theory. Equally important was the discovery of asymptotic freedom mentioned by Glashow. This discovery was more surprising than it may at first appear, as it suggests that the strength of the force between quarks gets weaker the closer the quarks are to each other. Exactly the opposite is true for electromagnetism, and it is fair to say that the discovery of asymptotic freedom in QCD was both surprising and profound. Not only does it allow one to perform calculations with the theory that allow its predications to be compared with experiment, but it also suggests that the strength of the force grows with distance. This, in turn, provides a physical motivation to assume that confinement is also a property of QCD, even though the mathematical calculations required to demonstrate this large distance property of the theory are currently beyond our abilities.
Anything but standard, Inference, vol 4, issue 2.
Thanks. If, as Krauss seems to say, Glashow’s article indeed left room to highlight that confinement is theoretically an open problem, that’s a good point to make.
(first I was confused about who is speaking here, now I suppose there is a typo in the subtitle: it should be “reply to” instead of “reply by”)
I am a little undecided whether Inference is the kind of citeable authorative source I was after. My starting point here was that everyone chats about the confinement problem, but that it seemed harder to find authorative sources officially declaring it an open problem. But I haven’t really been aware of Inference at all yet. Seems like a neat site.
I wonder if number theorists looking at non-abelian gauge groups in arithmetic gauge theory will find non-perturbative phenomena to parallel confinement.
So far there seems to be an argument specifically for an arithmetic version of Chern-Simons theory (only). Confinement is something in Yang-Mills theory.
Beware that physicists often say “gauge theory” when they really mean specifically Yang-Mills theory.
Perhaps Minhyong was only being suggestive when he said:
The work that occupies me most right now, arithmetic homotopy theory, concerns itself very much with arithmetic moduli spaces that are similar in nature and construction to moduli spaces of solutions to the Yang-Mills equation.
I see some number theorists are looking to relate the ABC conjecture and Yang-Mills theory arXiv:1602.01780.
One example of some Adelaide physicists looking at non-perturbative QCD seriously:
Professor Derek Leinweber; Professor Stephen Sharpe
Connecting Quantum Chromodynamics to experiment via non-perturbative effective field theory. This project aims to disclose the composition of proton excited states by advancing the theoretical formalism governing the underlying dynamics. At present, the structure of even the first excited state of the proton, the Roper, remains unknown for more than 50 years following its discovery. While the fundamental theory of Quantum Chromodynamics (QCD) describes the interactions between the quarks and gluons composing these states, the phenomena that emerge from QCD are complex and require dedicated analyses to understand them. The intended outcome is the creation of the effective field theory required to decipher QCD calculations.
This is from a grant, with its funding just awarded. The physics department here does do a lot of lattice QCD, though, so it is probably in that framework. But it made me read about the Roper resonance, which is not something I’d heard of before.
Thanks, interesting. Actually, their mentioning of “theoretical formalism governing the underlying dynamics” and of “the effective field theory required to decipher QCD calculations” indicates that they do mean to go beyond just lattice simulation. Might you have the full text for me?
Sadly that’s all that was publicly released. I might ask Derek, he was one of my lecturers and we talked last year briefly, but I’m not sure he’ll give it to me.
All right, if they just won that grant, then probably they’ll be setting up a website now for the project. Don’t go through any trouble, but if you happen hear to anything, I’d be interested.
added one more quote highlighting the open problem of confinement, from today’s
the entirety of the rich field of nuclear physics emerges from QCD: from the forces binding protons and neutrons into the nuclear landscape, to the fusion and fission reactions between nuclei, to the prospective interactions of nuclei with BSM physics, and to the unknown state of matter at the cores of neutron stars.
How does this emergence take place exactly? How is the clustering of quarks into nucleons and alpha particles realized? What are the mechanisms behind collective phenomena in nuclei as strongly correlated many-body systems? How does the extreme fine-tuning required to reproduce nuclear binding energies proceed? – are big open questions in nuclear physics.
added yet one more quote regarding the open problem:
Csaba Csaki, Matthew Reece, Toward a Systematic Holographic QCD: A Braneless Approach, JHEP 0705:062, 2007 (arxiv:hep-ph/0608266)
(in motivation of Ads/QCD)
QCD is a perennially problematic theory. Despite its decades of experimental support, the detailed low-energy physics remains beyond our calculational reach. The lattice provides a technique for answering nonperturbative questions, but to date there remain open questions that have not been answered
added one more to the list of quotes on the open problem:
many of the essential properties that the theory $[$QCD$]$ is presumed to have, including confinement, dynamical mass generation, and chiral symmetry breaking, are only poorly understood. And apart from the low-lying bound states of heavy quarks, which we believe can be described by a nonrelativistic Schroedinger equation, we are unable to derive from the basic theory even the grossest features of the pa~ticle spectrum, or of traditional strong interaction phenomenology
added yet one more quote on highlighting the confinement problem:
The problem with a derivation of nuclear forces from QCD is that this theory is non-perturbative in the low-energy regime characteristic of nuclear physics, which makes direct solutions very difficult. Therefore, during the first round of new attempts, QCD-inspired quark models became popular. The positive aspect of these models is that they try to explain hadron structure and hadron-hadron interactions on an equal footing and, indeed, some of the gross features of the nucleon-nucleon interaction are explained successfully. However, on a critical note, it must be pointed out that these quark-based approaches are nothing but another set of models and, thus, do not represent fundamental progress. For the purpose of describing hadron-hadron interactions, one may equally well stay with the simpler and much more quantitative meson models.
added yet one more quote:
Still after many decades of vigorous studies the outstanding challenge of modern physics is to establish a rigorous link of QCD to low-energy hadron physics as it is observed in the many experimental cross section measurements.
yet one more quote:
There are theoretical attempts to connect the fundamental theory of QCD with the very successful meson picture at low energy. The Skyrme model is an example. In other attempts, one tries to derive the NN interaction more or less directly from QCD. At present, the predictions are more of a qualitative kind. For quantitative results, the one-pion and two-pion contributions have to be added by hand, as they do not emerge naturally out of QCD-inspired models. Knowing that $\pi$ and $2\pi$ are the most important parts of the nuclear force, this defect of present quark model calculations is serious.
added yet one more quote on the confinement problem being open, here a basic gauge theory textbook:
Section 13.1.9:
The holy grail of QCD is the proof that a color SU(3) gauge theory confines in the non-perturbative regime.
This is not difficult to show for lattices with large spacing; unfortunately, such a demonstration does not constitute a proof of QCD confinement: to do that we must also demonstrate that the same theory that confines at large lattice spacing (strong coupling) has a continuum limit (weak coupling) that is consistent with the asymptotically free short distance behavior of QCD.
and one more “holy grail”-quote:
the holy grail sought by particle/nuclear knights has been to verify the correctness of the “ultimate” theory of strong interactions – quantum chromodynamics (QCD).
The theory is, of course, deceptively simple on the surface. $[...]$ So why are we still not satisfied? While at the very largest energies, asymptotic freedom allows the use of perturbative techniques, for those who are interested in making contact with low energy experimental findings there exist at least three fundamental difficulties:
i) QCD is written in terms of the “wrong” degrees of freedom – quarks and gluons – while low energy experiments are performed with hadronic boundstates;
ii) the theory is non-linear due to gluon self interactions;
iii) the theory is one of strong coupling so that perturbative methods are not practical
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