Integrable Superhierarchy of Discretized 2d Supergravity

TL;DR

This paper derives a hierarchy of nonlinear super-differential equations that describe the universal behavior of a discretized 2D supergravity model, connecting super Virasoro constraints with super KP hierarchy reductions.

Contribution

It introduces an integrable superhierarchy for discretized 2D supergravity by linking super Virasoro constraints with super KP hierarchy reductions through a double scaling limit.

Findings

Identified super-differential equations governing discretized 2D supergravity

Connected super Virasoro constraints with super KP hierarchy

Described the double-scaled constraints using a twisted scalar and Ramond fermion

Abstract

The hierarchical nonlinear super-differential equations are identified which describe universal behavior of the discretized model of $2d$ supergravity recently proposed. This is done by first taking a double scaling limit of the super Virasoro constraints ( at finite $N$) of the model and by rederiving it from the $\tilde{G}_{-1/2}$ constraint and the two reduction of the super KP hierarchy discussed. The double-scaled constraints are found to be described by a twisted scalar and a Ramond fermion.