The complex Liouville string: worldsheet boundaries and non-perturbative effects

TL;DR

This paper develops a universal formalism to relate boundary observables in complex Liouville string theory to closed string amplitudes, facilitating the study of non-perturbative effects and dualities with matrix models.

Contribution

It introduces a formalism that reduces boundary observables to closed string amplitudes, applicable across various string theories, and applies it to analyze non-perturbative effects and dualities.

Findings

Unified approach to boundary and closed string observables

Explicit boundary conditions for matrix model quantities

Insights into non-perturbative effects via ZZ-instantons

Abstract

We investigate general observables of the complex Liouville string with worldsheet boundaries. We develop a universal formalism that reduces such observables to ordinary closed string amplitudes without boundaries, applicable to any worldsheet string theory, but particularly simple in the context of 2d or minimal string theories. We apply this formalism to the duality of the complex Liouville string with the matrix integral proposed in arXiv:2409.18759 and arXiv:2410.07345 and showcase the formalism by finding appropriate boundary conditions for various matrix model quantities of interest, such as the resolvent or the partition function. We also apply this formalism towards the computation of non-perturbative effects on the worldsheet mediated by ZZ-instantons. These are known to be plagued by extra subtleties which need input from string field theory to resolve. These computations probe and uncover the duality between the complex Liouville string and the matrix model at the non-perturbative level.