Two-dimensional Yang-Mills Theories Are String Theories

TL;DR

This paper demonstrates that two-dimensional SO(N) and Sp(N) Yang-Mills theories can be interpreted as string theories, with their 1/N expansion corresponding to sums over maps from string worldsheets to the manifold, including nonorientable surfaces.

Contribution

It establishes a string theory interpretation for SO(N) and Sp(N) Yang-Mills theories, extending previous work on SU(N) theories to include nonorientable worldsheets and odd powers of 1/N.

Findings

Partition function expansion corresponds to string maps.

Includes both orientable and nonorientable worldsheets.

Maps are unbranched and branched covers with infinitesimal cross-caps.

Abstract

We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold M can be associated with maps from a string worldsheet onto M. These maps are unbranched and branched covers of M with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in M. These string theories differ from SU(N) Yang-Mills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets.