Topological contributions in two-dimensional Yang-Mills theory: from group averages to integration over algebras

TL;DR

This paper demonstrates that in 2D Yang-Mills theory, focusing on topologically trivial contributions simplifies the average of class functions on U(N) to an algebra integration, using geometric and instanton methods.

Contribution

It introduces a novel geometric approach to relate topologically trivial averages to algebra integrations in 2D Yang-Mills theory.

Findings

Topologically trivial contributions correspond to algebra integrations.

Decompactification of instanton expansions simplifies calculations.

Geometric procedures provide new insights into topological effects.

Abstract

We show that keeping only the topologically trivial contribution to the average of a class function on U(N) amounts to integrating over its algebra. The goal is reached first by decompactifying an expansion over the instanton basis and then directly, by means of a geometrical procedure.