Comment on Two Dimensional O(N) and Sp(N) Yang Mills Theories as String Theories

TL;DR

This paper develops a string theory interpretation for two-dimensional O(N) and Sp(N) Yang Mills theories by analyzing large N expansions and relating them to worldsheet configurations, extending previous U(N) results.

Contribution

It provides a complete large N expansion for O(N) and Sp(N) Yang Mills theories and interprets these in terms of string worldsheet configurations, expanding the understanding of gauge-string duality.

Findings

All orders large N expansions for O(N) and Sp(N) representations are derived.

Interpretation of expansion terms as symmetry factors for worldsheet configurations is established.

Connections to U(N) case and their implications are discussed.

Abstract

We write down all orders large $N$ expansions for the dimensions of irreducible representations of $O(N)$ and $Sp(N)$. We interpret all the terms in these expansions as symmetry factors for singular worldsheet configurations, involving collapsed crosscaps and tubes. We use it to complete the interpretation of two dimensional Yang Mills Theories with these gauge groups, on arbitrary two dimensional manifolds, in terms of a String Theory of maps of the type considered by Gross and Taylor. We point out some intriguing similarities to the case of $U(N)$ and discuss their implications.