Residues and Topological Yang-Mills Theory in Two Dimensions

TL;DR

This paper derives a residue formula for calculating correlation functions in two-dimensional topological SU(n) Yang-Mills theory, explores deformations, and introduces a diagonalization method to compute physical quantities, including handle contraction operators and genus recursion relations.

Contribution

It introduces a residue formula for correlation functions in 2D topological Yang-Mills theory and develops a diagonalization method for physical computations.

Findings

Derived a residue formula for correlation functions with magnetic flux

Analyzed deformations by two-form operators in detail

Identified an operator for handle contraction and established a genus recursion relation

Abstract

A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in some detail. The method of the diagonalization of a matrix valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.