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arXiv · 2610.35286

Log-Sobolev inequality for 2D $\mathrm{SU}(N)$ lattice gauge theory at all couplings

Jack Piazza·Hao Shen
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Abstract

We prove that the log-Sobolev inequality holds for the two-dimensional $SU(N)$ Wilson lattice Yang--Mills measure with arbitrary fixed inverse coupling $β$. The log-Sobolev constant depends on $β$ and $N$, but is uniform in the volume of the underlying lattice. The proof relies on a two-scale disintegration argument.

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Jack Piazza, Hao Shen. 2026-10-26. Log-Sobolev inequality for 2D $\mathrm{SU}(N)$ lattice gauge theory at all couplings. https://arxiv.org/abs/2610.35286

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