Branes, Rings and Matrix Models in Minimal (Super)string Theory

TL;DR

This paper provides a geometric framework using Riemann surfaces and matrix models to unify the description of bosonic and supersymmetric minimal string theories, analyzing branes and their relations.

Contribution

It introduces a unified geometric description of minimal string theories via Riemann surfaces and matrix models, connecting branes to line integrals and singularities.

Findings

FZZT and ZZ branes correspond to line integrals on Riemann surface M_{p,q}

Finite number of (m,n) ZZ branes located at singularities of M_{p,q}

Bosonic and supersymmetric theories with odd, coprime (p,q) may be equivalent

Abstract

We study both bosonic and supersymmetric (p,q) minimal models coupled to Liouville theory using the ground ring and the various branes of the theory. From the FZZT brane partition function, there emerges a unified, geometric description of all these theories in terms of an auxiliary Riemann surface M_{p,q} and the corresponding matrix model. In terms of this geometric description, both the FZZT and ZZ branes correspond to line integrals of a certain one-form on M_{p,q}. Moreover, we argue that there are a finite number of distinct (m,n) ZZ branes, and we show that these ZZ branes are located at the singularities of M_{p,q}. Finally, we discuss the possibility that the bosonic and supersymmetric theories with (p,q) odd and relatively prime are identical, as is suggested by the unified treatment of these models.