Two dimensional topological strings and gauge theory

Abstract

We study topological A-type string on an arbitrary two dimensional target space. Using the Virasoro constraints, proven by A. Okounkov and R. Pandharipande, we find an explicit formula for the partition function. The target space field theory reproducing this partition function is proposed. This field theory has infinite set of deformations which are overlooked by the standard definition of the topological string. We also discuss the relations to the multi-trace deformations of gauge theories, and make contact with quantum integrable systems. In addition, the target space theory can be in turn coupled to gravity, thereby realizing the topological string version of M. Green's "worldsheets for worldsheets" idea.