Holomorphic maps and the complete 1/N expansion of 2D SU(N) Yang-Mills

TL;DR

This paper describes the complete 1/N expansion of 2D SU(N) Yang-Mills theory using the moduli space of holomorphic maps, connecting it to algebraic structures and Euler characteristics of moduli spaces.

Contribution

It provides a geometric and algebraic framework for understanding the 1/N expansion of 2D Yang-Mills theory through holomorphic maps and moduli space analysis.

Findings

Relation between Euler characters of different moduli spaces

Connection to Gross-Taylor 1/N expansion via Brauer and symmetric groups

Description of the 1/N expansion in terms of holomorphic maps from worldsheets

Abstract

We give a description of the complete 1/N expansion of SU(N) 2D Yang Mills theory in terms of the moduli space of holomorphic maps from non-singular worldsheets. This is related to the Gross-Taylor coupled 1/N expansion through a map from Brauer algebras to symmetric groups. These results point to an equality between Euler characters of moduli spaces of holomorphic maps from non-singular worldsheets with a target Riemann surface equipped with markings on the one hand and Euler characters of another moduli space involving worldsheets with double points (nodes).