Superloop Equations and Two Dimensional Supergravity

TL;DR

This paper introduces a discrete model that captures the critical behavior of certain superconformal models coupled to 2D supergravity, providing new insights into their integrable structures and correlation functions.

Contribution

It presents a novel discrete model with super-Virasoro constraints that reproduces key features of supergravity coupled models and identifies a supersymmetric integrable hierarchy.

Findings

Reproduces string susceptibility and scaling dimensions of superconformal models

Evaluates all planar loop correlation functions in the continuum limit

Identifies a supersymmetric generalization of the KP hierarchy

Abstract

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of $(2,4m)$-minimal superconformal models coupled to $2D$-supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of non-linear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.