Unitary-Matrix Integration on 2D Yang-Mills Action

TL;DR

This paper introduces a novel method for integrating 2D Yang-Mills action using unitary-matrix integration and the Itzykson-Zuber integral, simplifying the calculation by reducing matrix integrals to vector integrals.

Contribution

It provides a new approach to perform unitary-matrix integration in 2D Yang-Mills theory leveraging the heat equation's uniqueness.

Findings

Derived explicit expressions for matrix integrations

Reduced matrix integrals to vector integrals

Validated the method's effectiveness in 2D Yang-Mills context

Abstract

Using the idea of Itzykson-Zuber integral, unitary-matrix integration of 2D Yang-Mills action is presented. The uniqueness of the solution of heat equation enables us to integrate out the unitary-matrix parts of hermite matrices and to obtain the expression of integration over vectors, also in this case.