Two-Dimensional Chiral Matrix Models and String Theories

TL;DR

This paper introduces and exactly solves a class of two-dimensional matrix gauge models that describe string theories with complex worldsheet ramification points, simplifying previous approaches to 2D Yang-Mills theory.

Contribution

It formulates a new class of solvable 2D matrix models representing string theories with ramification points, expanding the understanding of non-folding surface ensembles.

Findings

Exact solutions for models on arbitrary target space lattices

Simplification over previous 2D Yang-Mills string descriptions

Character expansion methods enable analytical solutions

Abstract

We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, discretized, two-dimensional manifold. We interpret the models as string theories characterized by a set of coupling constants associated to worldsheet ramification points of various orders. Our approach is closely related to, but simpler than, the string theory describing two-dimensional Yang-Mills theory. Using recently developed character expansion methods we exactly solve the models for target space lattices of arbitrary internal connectivity and topology.