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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 29th 2013

stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 15th 2013

added (very) brief pointers to confinement in N=2 D=4 super Yang-Mills theory (in both these entries)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJun 24th 2014
• (edited Jun 24th 2014)

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.)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 3rd 2014

Have expanded the list of references a little, with more on confinement via monopole condensation.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeApr 27th 2018

added pointer to today’s Simonov 18. Hm…

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeSep 20th 2018
• (edited Sep 20th 2018)

Added a section here here on the argument by Atiyah and Witten on how to prove confinement in $\mathcal{N} = 1$ super Yang-Mills via embedding it into M-theory in $G_2$-manifolds in two different but allegedly equivalent ways.

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeSep 20th 2018

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?

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 20th 2018
• (edited Sep 20th 2018)

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.

• CommentRowNumber9.
• CommentAuthorDavid_Corfield
• CommentTimeSep 20th 2018

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?

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeSep 20th 2018
• (edited Sep 20th 2018)

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.)

• CommentRowNumber11.
• CommentAuthorDavid_Corfield
• CommentTimeSep 20th 2018

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.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeOct 11th 2018