Time-dependent backgrounds of 2D string theory: Non-perturbative effects

TL;DR

This paper investigates non-perturbative corrections to the partition function of a 2D string theory in a time-dependent background, using matrix models and complex curve analysis to classify and compute these effects.

Contribution

It introduces a dual matrix quantum mechanics approach to calculate non-perturbative effects in time-dependent 2D string backgrounds, including sine-Liouville deformations.

Findings

Non-perturbative corrections classified by complex curve double points.

Explicit calculation of leading and subleading NPC using Toda equations.

Identification of NPC contributions with disk and annulus correlation functions.

Abstract

We study the non-perturbative corrections (NPC) to the partition function of a compactified 2D string theory in a time-dependent background generated by a tachyon source. The sine-Liouville deformation of the theory is a particular case of such a background. We calculate the leading as well as the subleading NPC using the dual description of the string theory as matrix quantum mechanics. As in the minimal string theories, the NPC are classified by the double points of a complex curve. We calculate them by two different methods: by solving Toda equation and by evaluating the quasiclassical fermion wave functions. We show that the result can be expressed in terms of correlation functions of the bosonic field associated with the tachyon source and identify the leading and the subleading corrections as the contributions from the one-point (disk) and two-point (annulus) correlation functions.