A Stochastic Analysis Approach to Lattice Yang--Mills
发布时间：2022年11月14日
浏览次数：3109
发布者: He Liu
主讲人： Rongchan Zhu(Beijing Institute of Technology)
活动时间： 从 2022-11-17 16:00 到 17:30
场地： 线上
We develop a new stochastic analysis approach to the lattice Yang--Mills model at strong coupling in any dimension $d>1$, with t' Hooft scaling $\beta N$ for the inverse coupling strength. We study their Langevin dynamics, ergodicity, functional inequalities, large $N$ limits, and mass gap.
Assuming $|\beta| < \frac{N-2}{32(d-1)N}$ for the structure group $SO(N)$, or $|\beta| < \frac{1}{16(d-1)}$ for $SU(N)$, we prove the following results. The invariant measure for the corresponding Langevin dynamic is unique on the entire lattice, and the dynamic is exponentially ergodic under a Wasserstein distance. The finite volume Yang--Mills measures converge to this unique invariant measure in the infinite volume limit, for which Log-Sobolev and Poincar\'e inequalities hold. These functional inequalities imply that the suitably rescaled Wilson loops for the infinite volume measure has factorized correlations and converges in probability to deterministic limits in the large $N$ limit, and correlations of a large class of observables decay exponentially, namely the infinite volume measure has a strictly positive mass gap. Our method improves earlier results or simplifies the proofs, and provides some new perspectives to the study of lattice Yang--Mills model.
腾讯会议链接：https://meeting.tencent.com/dm/Sex5wA235FZm
腾讯会议：181-547-808
会议密码：221117
