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

TL;DR

This paper establishes a connection between the 0A matrix model's free energy and topological string amplitudes, revealing geometric structures and relating matrix models to four-dimensional black holes in string theory.

Contribution

It introduces a novel geometric interpretation of the 0A matrix model's free energy and relates it explicitly to black hole entropy in type IIB string theory.

Findings

The free energy relates to topological and anti-topological string amplitudes.

A new geometric framework for the matrix model is proposed.

Explicit correspondence between matrix model free energy and black hole entropy.

Abstract

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.