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Today, Korean media is reporting that a team of South Korean researchers solved Yang-Mill existence and mass gap problem. Did anyone outside Korea even notice this? I was not able to notice anything in US media.

The paper is

Dimensional Transmutation by Monopole Condensation in QCD. Y. M. Cho, F. H. Cho, and J. H. Yoon. Phys. Rev. D. 87 no. 8, 085025 (2013). arXiv:1206.6936 [hep-th].

Is this just an ordinary "good" paper that is nothing close to solving Yang-Mills existence and mass gap problem? Or is it purported solution?

Note that the arxiv preprint is 2012's but the news of publication in Physical Review D is April, 2013.

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If "Today, Korean media [...]" and *"1206.6936" (which means June 2012 posting to the arXiv) really go together, then we already know why there is no big kerfuffle in the scientific community: that's old news (on order of 10 months). –  dmckee Apr 17 '13 at 12:47
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@dmckee Arxiv and Physica Review D dates difference. This probably means that either the paper had nothing to do with solving Yang-Mill existence and mass gap problem or people just did not notice then. –  Yang Apr 17 '13 at 12:50
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in any case, I will try to read the paper in minutes. –  Yang Apr 17 '13 at 13:07
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I don't have any idea what the paper is about. I only know that a 10 month old paper is unlikely to create a stir. You have to get used to the idea that mass media deals very poorly with science. Though science reporter generally understand at least some of what they are reporting on their bosses don't and they are writing for the least common denominator among their audience which is a pretty low level. –  dmckee Apr 17 '13 at 13:21
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Yongmin Cho has been pushing this idea for more than ten years e.g. arxiv.org/abs/hep-th/0301013 –  Mitchell Porter Apr 17 '13 at 15:50
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2 Answers

up vote 5 down vote accepted

First impressions based on a quick read of the preprint:

  • I'm out of my depth on this! I couldn't tell you if their derivation is correct, but assuming that it is:

  • They don't treat real QCD. They study SU(2) YM without quarks. The authors claim they can do real QCD and get the same result, but this is not demonstrated in the paper (they defer this to a later publication).

  • They derive the gauge invariant infrared finite effective action of this theory at one loop. This is surely an impressive achievement, and an important milestone if it's true, but is probably still far from what a mathematician would accept as a "proof."

  • With the above caveats they show that monopole-antimonopole condensation is responsible for confinement, and that the tachyons appearing in previous calculations are unphysical.

EDIT: user1504 mentions the Millenium Prize, which involves pure YM (with an arbitrary gauge group though). This paper definitely doesn't satisfy the prize conditions:

  • It uses the regular not entirely rigorous (i.e., not axiomatically formulated) definition of Yang-Mills theory used by physicists, and

  • It doesn't prove a mass gap. You need a calculation to all orders to do that to a mathematician's satisfaction.

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To be fair, the lattice gauge theory people use the same definition the mathematicians would: It's the QFT defined by the continuum limit of the YM lattice path integral. They're just less fussy about their approximations. –  user1504 Apr 17 '13 at 15:33
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The phrase 'Yang-Mills existence and mass gap' usually refers to a particular Millenium Prize Problem, which asks for

a) a rigorous mathematical construction of pure 4d Yang-Mills theory (gluons only, no quarks), and

b) a proof that the Hamiltonian of this theory has a mass gap.

There's a $1M prize for doing this, which is what the media tends to get excited about. But the prize is for mathematical proofs, and the paper you've linked to is a physics paper. It looks to me like a rather interesting physics paper, but it definitely isn't a rigorous non-perturbative treatment of Yang-Mills theory. (They make no indication that their approximations are under analytic control.) It isn't going to win the Millenium prize.

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