Black Hole Entropy, Marginal Stability and Mirror Symmetry

TL;DR

This paper explores the microscopic origin of black hole entropy in type IIB Calabi-Yau compactifications by analyzing superconformal quantum mechanics, marginal stability, and mirror symmetry, providing explicit entropy calculations in specific models.

Contribution

It introduces a novel approach to compute black hole microstates using mirror symmetry and T-dualities, extending previous methods to new geometries and cases.

Findings

Explicit microscopic entropy calculations for certain black holes.

Demonstration of mirror symmetry and T-dualities in counting microstates.

Application of Fourier-Mukai transform in K3xT^2 case.

Abstract

We consider the superconformal quantum mechanics associated to BPS black holes in type IIB Calabi-Yau compactifications. This quantum mechanics describes the dynamics of D-branes in the near-horizon attractor geometry of the black hole. In many cases, the black hole entropy can be found by counting the number of chiral primaries in this quantum mechanics. Both the attractor mechanism and notions of marginal stability play important roles in generating the large number of microstates required to explain this entropy. We compute the microscopic entropy explicitly in a few different cases, where the theory reduces to quantum mechanics on the moduli space of special Lagrangians. Under certain assumptions, the problem may be solved by implementing mirror symmetry as three T-dualities: this is essentially the mirror of a calculation by Gaiotto, Strominger and Yin. In some simple cases, the calculation may be done in greater generality without resorting to conjectures about mirror symmetry. For example, the K3xT^2 case may be studied precisely using the Fourier-Mukai transform.