Almost flat highest weights and application to Wilson loops on compact surfaces

Abstract

We develop several properties of the almost flat highest weights of U(N ) and SU(N ) introduced in a previous paper [Lem21], and use them to compute the limit of the expectation and variance of Wilson loops associated with contractible simple loops on compact orientable surfaces with genus 1 and higher. As such, it provides a purely representation-theoretic proof for the main result of in [DL22] in the case of unitary groups.