The Supereigenvalue Model in the Double-Scaling Limit

TL;DR

This paper analyzes the double-scaling limit of the supereigenvalue model using moment description, identifying multi-critical points and developing an iterative method for calculating higher-genus contributions to free energy and correlators.

Contribution

It introduces a moment-based approach to study the double-scaling limit and provides explicit higher-genus calculations up to genus two.

Findings

Identification of multi-critical points in coupling constant space

Development of an iterative procedure for higher-genus calculations

Explicit genus two results for free energy and correlators

Abstract

The double-scaling limit of the supereigenvalue model is performed in the moment description. This description proves extremely useful for the identification of the multi-critical points in the space of bosonic and fermionic coupling constants. An iterative procedure for the calculation of higher-genus contributions to the free energy and to the multi-loop correlators in the double-scaling limit is developed. We present the general structure of these quantities at genus g and give explicit results up to and including genus two.