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

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.