Type 0A matrix model of a black hole, integrability, and holography

Abstract

We investigate a deformed matrix model of type 0A theory related to supersymmetric Witten's black hole in two-dimensions, a generalization of bosonic model suggested by Kazakov et al. We find a free field realization of the partition function of the matrix model, which includes Ramond-Ramond perturbations in the type 0A theory. In a simple case, the partition function is factorized into two determinants, which are given by tau function of an integrable system. We work out the genus expansion of the partition function. Holographic relation with the supersymmetric Witten's black hole is checked by Wilson line computation. The corresponding partition function of the matrix model exhibits a singular behavior, which is interpreted as the point of enhanced N=2 world sheet supersymmetry. An interesting relation between the deformed matrix model and topological string on a Z(2) orbifold of conifold is found.