Non-critical superstrings: a comparison between continuum and discrete approaches

TL;DR

This paper compares continuum and discrete approaches to non-critical superstrings, focusing on supersymmetric Liouville theory and matrix models, and extends previous relations to the supersymmetric case with new formulations and wave equations.

Contribution

It introduces a supersymmetric extension of the matrix model and Liouville approach, including a minisuperspace approximation and wave equation for non-critical superstrings.

Findings

Extended the relation between matrix models and Liouville theory to supersymmetric cases

Formulated the minisuperspace approximation for supersymmetric models

Derived the wave equation for supersymmetric non-critical superstrings

Abstract

We review the relation between the matrix model and Liouville approaches to two-dimensional gravity as elaborated by Moore, Seiberg and Staudacher. Then, based on the supersymmetric Liouville formulation and the discrete eigenvalue model proposed by Alvarez-Gaum\'e, Itoyama, Ma\~nes and Zadra, we extend the previous relation to the supersymmetric case. The minisuperspace approximation for the supersymmetric case is formulated, and the corresponding wave equation is found.