论文标题
多项式和矩的期望值一般紧凑的谎言组
Expectation values of polynomials and moments on general compact Lie groups
论文作者
论文摘要
我们开发了一个强大的框架，以基于基本表示理论参数和按零件公式的集成来计算紧凑型谎言组的多项式和矩的期望值。在晶格量规理论的设置中，我们将Chatterjee和Jafarov的Wilson Loops产品的期望值公式推广到任意紧凑的Lie群体，并研究许多经典紧凑的Lie lie组的明确例子和杰出的Lie lie组和$ G_2 $。通过Collins和Lévy扩展经典结果，我们使用框架来得出在HAAR度量，Brownian Motion和Wilson Action下的基质系数多项式的期望值公式。特别是，我们通过研究基本张量不变性来为一般紧凑型谎言组构建Weingarten功能，并将其应用于$ \ Mathrm {su}（n）$和$ g_2 $。
We develop a powerful framework to calculate expectation values of polynomials and moments on compact Lie groups based on elementary representation-theoretic arguments and an integration by parts formula. In the setting of lattice gauge theory, we generalize expectation value formulas for products of Wilson loops by Chatterjee and Jafarov to arbitrary compact Lie groups, and study explicit examples for many classical compact Lie groups and the exceptional Lie group $G_2$. Extending classical results by Collins and Lévy, we use our framework to derive expectation value formulas of polynomials of matrix coefficients under the Haar measure, Brownian motion, and the Wilson action. In particular, we construct Weingarten functions for general compact Lie groups by studying the underlying tensor invariants, and apply this to $\mathrm{SU}(N)$ and $G_2$.
