The String Theory Approach to Generalized 2D Yang-Mills Theory

TL;DR

This paper derives a string theory representation for generalized 2D Yang-Mills theory on arbitrary surfaces, extending known formulas and highlighting the role of complex string maps with branch points.

Contribution

It provides a novel stringy description of generalized 2D Yang-Mills theory, generalizing the Rusakov formula and incorporating higher-degree branch points.

Findings

Derived a sum-over-representations formula for the partition function.

Established a Gross-Taylor like string expansion for the model.

Identified the significance of higher-degree branch points in the string maps.

Abstract

We calculate the partition function of the $SU(N)$ ( and $U(N)$) generalized $YM_2$ theory defined on an arbitrary Riemann surface. The result which is expressed as a sum over irreducible representations generalizes the Rusakov formula for ordinary YM_2 theory. A diagrammatic expansion of the formula enables us to derive a Gross-Taylor like stringy description of the model. A sum of 2D string maps is shown to reproduce the gauge theory results. Maps with branch points of degree higher than one, as well as ``microscopic surfaces'' play an important role in the sum. We discuss the underlying string theory.