Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-07-27
Class.Quant.Grav.23:S981,2006
Physics
High Energy Physics
High Energy Physics - Theory
103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important upgrade, prepared for the proceedings of Frascati School on
Scientific paper
10.1088/0264-9381/23/21/S05
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.
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