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I was just reminded of John Baez years ago describing Bar-Natan’s paper on the four-color problem and the relation between $SU(2)$ and $SU(n)$ gauge theory. Bar-Natan’s paper is here.
Thanks, excellent. So let’s add that to all related entries:
On the logical equivalence between the four-colour theorem and a statement about transition from the small N limit to the large N limit for Lie algebra weight systems on Jacobi diagrams via the ’t Hooft double line construction:
I wonder if Bar-Natan didn’t know that the double line construction he uses so effectively is earlier due to ’t Hooft, or if he intentionally chose to never cite him. Seems a curious omission.
That would be fun if M-theory could help out with the four-colour problem!
added this pointer on 1/N corrections in 2d QCD:
added this pointer:
added pointer to
added pointer to today’s:
added pointer to:
with this quote:
26:26: “by now it’s clear [Lucini & Teper 2001] that lattice gauge theory, at least for the glueball sector, has made it clear that the $1/N$-expansion is a good approximation to the real world, especially if you include a leading correction to the large $N$ limit. Now unfortunately this is best established in the glueball sector, which is not very accessible experimentally.”
28:56: “but the $1/N$ expansion doesn’t explain everything. In fact, it’s not hard to find phenomena in meson physics where the $1/N$-expansion does not work well.”
36:15: “I suspect the $1/N$-expansion works reasonably well for many aspects of baryons. However, as for mesons, it is easy to point to things that won’t work well for baryons. In particular, among other things, I don’t think the $1/N$ expansion will be successful for nuclei as opposed to individual nucleons.”
37:12: “I don’ t think the phenomenological models used by nuclear physicists would have any success at of if the large N limit was a good description of nuclei.”
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