On the String Actions for the Generalized Two-dimensional Yang-Mills Theories

TL;DR

This paper explores the structure of partition functions in large N generalized 2D Yang-Mills theories, extending topological string models to include higher Casimir operators and introducing deformed gravitational descendants.

Contribution

It provides new operator expressions for higher Casimir terms in gYM_2 and extends the topological string framework to these theories.

Findings

Derived expressions for higher Casimir operators in gYM_2

Extended topological string models to include generalized 2D Yang-Mills theories

Introduced the concept of deformed gravitational descendants

Abstract

We study the structures of partition functions of the large $N$ generalized two-dimensional Yang-Mills theories ($gYM_2$) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam's topological string model describing the ordinary $YM_2$ \cite{CMR} to those describing $gYM_2$. We present the expressions of the appropriate operators to reproduce the higher Casimir terms in $gYM_2$. The concept of ''deformed gravitational descendants'' will be introduced for this purpose.