Deformed type 0A matrix model and super-Liouville theory for fermionic black holes

We consider a ${\hat c}=1$ model in the fermionic black hole background. Forthis purpose we consider a model which contains both the N=1 and the N=2super-Liouville interactions. We propose that this model is dual to a recentlyproposed type 0A matrix quantum mechanics model with vortex deformations. Wesupport our conjecture by showing that non-perturbative corrections to the freeenergy computed by both the matrix model and the super-Liouville theories agreeexactly by treating the N=2 interaction as a small perturbation. We also showthat a two-point function on sphere calculated from the deformed type 0A matrixmodel is consistent with that of the N=2 super-Liouville theory when the N=1interaction becomes small. This duality between the matrix model andsuper-Liouville theories leads to a conjecture for arbitrary $n$-pointcorrelation functions of the N=1 super-Liouville theory on the sphere.Comment: 18 pages, no figur