Deformed Type 0A Matrix Model and Super-Liouville Theory for Fermionic Black Holes

TL;DR

This paper proposes a duality between a deformed type 0A matrix model with vortex deformations and a super-Liouville theory in a fermionic black hole background, supported by matching non-perturbative corrections and correlation functions.

Contribution

It introduces a duality between a deformed type 0A matrix model and N=1, N=2 super-Liouville theories, providing evidence through non-perturbative corrections and correlation functions.

Findings

Non-perturbative free energy corrections match between models

Two-point functions are consistent in the dual theories

Conjecture for arbitrary n-point correlation functions

Abstract

We consider a ${\hat c}=1$ model in the fermionic black hole background. For this purpose we consider a model which contains both the N=1 and the N=2 super-Liouville interactions. We propose that this model is dual to a recently proposed type 0A matrix quantum mechanics model with vortex deformations. We support our conjecture by showing that non-perturbative corrections to the free energy computed by both the matrix model and the super-Liouville theories agree exactly by treating the N=2 interaction as a small perturbation. We also show that a two-point function on sphere calculated from the deformed type 0A matrix model is consistent with that of the N=2 super-Liouville theory when the N=1 interaction becomes small. This duality between the matrix model and super-Liouville theories leads to a conjecture for arbitrary $n$-point correlation functions of the N=1 super-Liouville theory on the sphere.