Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)

TL;DR

This paper reviews recent advances in understanding the microscopic and macroscopic entropy of four-dimensional BPS black holes, exploring topological string theory, the OSV conjecture, and quantum attractors beyond the large charge limit.

Contribution

It introduces a systematic approach to quantum attractors and proposes a general framework for automorphic partition functions related to black hole degeneracies.

Findings

Validation of the OSV conjecture on small black holes

Development of a quantum attractor framework

Proposal of a one-parameter generalization of topological string amplitude

Abstract

In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a brief overview of charged black holes in supergravity and string theory, we give an extensive introduction to special and very special geometry, attractor flows and topological string theory, including holomorphic anomalies. We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates microscopic degeneracies to the topological string amplitude, and review precision tests of this formula on ``small'' black holes. Finally, motivated by a holographic interpretation of the OSV conjecture, we give a systematic approach to the radial quantization of BPS black holes (i.e. quantum attractors). This suggests the existence of a one-parameter generalization of the topological string amplitude, and provides a general framework for constructing automorphic partition functions for black hole degeneracies in theories with sufficient degree of symmetry.