Minimal Superstrings and Loop Gas Models

TL;DR

This paper reformulates minimal superstring matrix models as loop gas models on random surfaces, clarifying their connection to bosonic string theories and elucidating the role of RR operators and spin structures.

Contribution

It introduces a loop gas model framework for minimal superstrings, providing new insights into their structure and relation to bosonic strings, including open strings and RR operators.

Findings

Minimal superstrings correspond to specific bosonic string theories.

Loop gas models naturally incorporate spin structures and RR operators.

Open string boundary conditions are clarified in the loop gas formulation.

Abstract

We reformulate the matrix models of minimal superstrings as loop gas models on random surfaces. In the continuum limit, this leads to the identification of minimal superstrings with certain bosonic string theories, to all orders in the genus expansion. RR vertex operators arise as operators in a Z_2 twisted sector of the matter CFT. We show how the loop gas model implements the sum over spin structures expected from the continuum RNS formulation. Open string boundary conditions are also more transparent in this language.