# Is gauge theory at long distances described by strong-coupling expansion?

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In communication here, on the site, Marco Frasca has suggested to me that recent results from lattice groups show that the gauge theory at long distances is not described accurately by the predictions from Wilson's strong coupling expansion.

To remind folks what these predictions are: infinitely strong coupling at long distances implies that the statistics of any gauge configuration in a volume V is completely statistically independent of the configuration of the gauge field in volume U, when the minimum distance between a point in V and U is larger than several times the confinement length. It predicts that all correlators between the two regions (in a gauge unfixed simulation) vanish exponentially as the distance times $\Lambda$, so that the configuration on a coarse lattice is completely random.

What this means precisely is that if you take the product of the gauge field associated with n consecutive links in the same direction (gauge unfixed simulation), the result when the transport is over a size many times larger than the confinement length is a completely random element of the gauge group, chosen according to Haar measure.

The strong coupling fixed point, completely uncorrelated gauge fields, should describe any pure SU(N) gauge theory simulation (no quarks, they can make nearly massless pions which produce powerlaw correlations). Not only this, but the strong coupling expansion describes the rate of relaxation to this uncorrelated long-distance state.

I personally not only think that these claims are accurate, I also think they should not be hard to establish rigorously.

What specific claims in the recent lattice literature are claimed to cast doubt on this picture? I have not seen a specific paper which claims that this picture is false explicitly, but there seems to be this implication floating in the air. I would like to understand why.

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