Complex curves and non-perturbative effects in c=1 string theory

TL;DR

This paper explores a complex curve in c=1 string theory, providing a geometric understanding of D-branes, non-perturbative effects, and their origins, through matrix model formulation and perturbations.

Contribution

It introduces a new geometric framework for understanding D-branes and non-perturbative effects in c=1 string theory using complex curves and matrix models.

Findings

Identified singularities with ZZ branes.

Derived non-perturbative corrections to free energy.

Linked corrections to conformal field theory origins.

Abstract

We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation removes the degeneracy of the non-perturbed curve and allows to identify its singularities with ZZ branes. Also, using the constructed curve, we find non-perturbative corrections to the free energy and elucidate their CFT origin.