Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds

TL;DR

This paper explores the connection between matrix models, topological strings, and 4D black hole entropy, demonstrating how matrix models can compute black hole entropy in non-compact Calabi-Yau settings.

Contribution

It establishes a detailed link between c=1 matrix models and topological strings on non-compact Calabi-Yau manifolds, enabling entropy calculations for 4D black holes.

Findings

Black hole entropy matches matrix model free energy up to a constant.

Divergences from non-compactness are effectively managed.

The deformed matrix model provides detailed insights into black hole microstates.

Abstract

We study the relation between c=1 matrix models at self-dual radii and topological strings on non-compact Calabi-Yau manifolds. In particular the special case of the deformed matrix model is investigated in detail. Using recent results on the equivalence of the partition function of topological strings and that of four dimensional BPS black holes, we are able to calculate the entropy of the black holes, using matrix models. In particular, we show how to deal with the divergences that arise as a result of the non-compactness of the Calabi-Yau. The main result is that the entropy of the black hole at zero temperature coincides with the canonical free energy of the matrix model, up to a proportionality constant given by the self-dual temperature of the matrix model.