Expectation values of polynomials and moments on general compact Lie groups
Published in arXiv, 2022
This paper is a collaboration with Tobias Diez, and is available on arXiv: Click!
Abstract: 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 G2. 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 SU(N) and G2.