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

TL;DR

This paper studies a deformed type 0A matrix model related to supersymmetric black holes in two dimensions, revealing integrability, holography, and connections to topological strings, with explicit partition function analysis and supersymmetry enhancement.

Contribution

It introduces a free field realization of the deformed matrix model's partition function, demonstrating integrability, holographic correspondence, and links to topological string theory.

Findings

Partition function factorizes into determinants related to integrable systems

Holographic relation confirmed via Wilson line computations

Partition function shows singular behavior indicating enhanced supersymmetry

Abstract

We investigate a deformed matrix model of type 0A theory related to supersymmetric Witten's black hole in two-dimensions, 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. Corresponding partition function of the matrix model exhibits a singular behavior, which is interpreted as the point of enhanced ${\cal N}=2$ worldsheet supersymmetry. Interesting relation of the deformed matrix model and topological string on a $Z_2$ orbifold of conifold is found.