4D black holes and holomorphic factorization of the 0A matrix model

In this letter, we relate the free energy of the 0A matrix model to the sum of topological and anti-topological string amplitudes. For arbitrary integer multiples of the matrix model self-dual radius we describe the geometry on which the corresponding topological string propagates. This geometry is not the one that follows from the usual ground ring analysis, but in a sense its "holomorphic square root". Mixing of terms for different genus in the matrix model free energy yields one-loop terms compatible with type II strings on compact Calabi-Yau target spaces. As an application, we give an explicit example of how to relate the 0A matrix model free energy to that of a four-dimensional black hole in type IIB theory, compactified on a compact Calabi-Yau. Variables, Legendre transforms, and large classical terms on both sides match perfectly.