Instantons in sine-Liouville theory

TL;DR

This paper calculates instanton effects in sine-Liouville theory, a model for 2D string theory with tachyon backgrounds, using both matrix models and conformal field theory, and finds consistent results across methods.

Contribution

It provides the first detailed comparison of instanton corrections in sine-Liouville theory using matrix models and string theory techniques, including non-perturbative effects in the perturbation parameter.

Findings

Matrix model results match string theory in small  expansion.

Derived analytic predictions for disk two-point functions with ZZ boundary conditions.

Extended analysis to multiple tachyon vertex operators with different momenta.

Abstract

We compute instanton corrections to the partition function of sine-Liouville (SL) theory, which provides a worldsheet description of two-dimensional string theory in a non-trivial tachyon background. We derive these corrections using a matrix model formulation based on a chiral representation of matrix quantum mechanics and using string theory methods. In both cases we restrict to the leading and subleading orders in the string coupling expansion. Then the CFT technique is used to compute two orders of the expansion in the SL perturbation parameter $\lambda$, while the matrix model gives results which are non-perturbative in $\lambda$. The matrix model results perfectly match those of string theory in the small $\lambda$ expansion. We also generalize our findings to the case of perturbation by several tachyon vertex operators carrying different momenta, and obtain interesting analytic predictions for the disk two-point and annulus one-point functions with ZZ boundary condition.