Nonperturbative Solution of the Super-Virasoro Constraints

TL;DR

This paper provides a nonperturbative solution to the super-Virasoro constraints, connecting them to the one-matrix model and exploring their behavior in the double scaling limit, with some discrepancies noted in supersymmetric KdV extensions.

Contribution

It offers the first nonperturbative solution of the super-Virasoro constraints and links them to matrix models, advancing understanding of supersymmetric quantum gravity.

Findings

Solution of super-Virasoro constraints to all orders of genus expansion.

Representation of the partition function via the one-matrix model.

Discrepancies between flows and known supersymmetric KdV extensions.

Abstract

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the nonperturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.