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

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.

103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important upgrade, prepared for the proceedings of Frascati School on Attractor Mechanism; Sec 7 was largely rewritten to incorporate recent progress; more figures, more refs, and minor changes in abstract and introduction

References in corpus (2)

• Strings, Black Holes, and Quantum Information
• Stringy Black Holes and the Geometry of Entanglement

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• Erice Lectures on Black Holes and Attractors
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• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• 4d/5d Correspondence for the Black Hole Potential and its Critical Points
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• Black-Hole Attractors in N=1 Supergravity
• Black Hole Entropy and Finite Geometry
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• Large D-instanton effects in string theory
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• alpha'^2-corrections to extremal dyonic black holes in heterotic string theory
• Arrow of Time in String Theory
• Black Hole Giants
• Cargese lectures on string theory with eight supercharges
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• (p,q)-form Kaehler Electromagnetism