A Stochastic Analysis Approach to Lattice Yang–Mills at Strong Coupling
A Stochastic Analysis Approach to Lattice Yang–Mills at Strong Coupling
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DOI：
10.1007/s00220-022-04609-1
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发表时间：
2022-04
影响因子：
2.4
通讯作者：
Hao Shen;Rongchan Zhu;Xiangchan Zhu
中科院分区：
文献类型：
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作者：
Hao Shen;Rongchan Zhu;Xiangchan Zhu
我们开发了一种新的随机分析方法，用于任何维度强耦合的格子 Yang-Mills 模型，并使用 t’ Hooft 缩放来计算逆耦合强度。我们研究它们的朗之万动力学、遍历性、函数不等式、大N极限和质量间隙。假设对于结构群SO(N)，或者对于SU(N)，我们证明以下结果。相应的 Langevin 动力学的不变测度在整个格子上是唯一的，并且该动力学在 Wasserstein 距离下呈指数遍历。有限体积杨-米尔斯测度收敛到无限体积极限中的这种独特的不变测度，Log-Sobolev 和庞加莱不等式成立。这些函数不等式意味着无限体积测度的适当重新标度的威尔逊环具有因式分解的相关性，并且在概率上收敛到largeNlimit中的确定性极限，并且一大类可观测量的相关性呈指数衰减，即无限体积测度具有严格的正质量间隙。我们的方法改进了早期的结果或简化了证明，为格子Yang-Mills模型的研究提供了一些新的视角。
We develop a new stochastic analysis approach to the lattice Yang–Mills model at strong coupling in any dimension, with t’ Hooft scalingfor the inverse coupling strength. We study their Langevin dynamics, ergodicity, functional inequalities, largeNlimits, and mass gap. Assumingfor the structure groupSO(N), orforSU(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 Poincaré 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 largeNlimit, 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.