From Special Geometry to Black Hole Partition Functions

TL;DR

This paper explores the connection between special geometry and black hole partition functions, focusing on attractor mechanisms, BPS black holes, and string compactifications, providing both physical insights and mathematical foundations.

Contribution

It offers a comprehensive review of special geometry, attractor mechanisms, and black hole partition functions from both physical and mathematical perspectives.

Findings

Analysis of BPS black holes in N=4 supergravity

Development of the variational principle for black hole entropy

Connection between modular forms and state counting in string theory

Abstract

These notes are based on lectures given at the Erwin-Schrodinger Insitut in Vienna in 2006/07 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I: special geometry from the superconformal point of view. Lecture II: black hole attractor mechanism, its underlying variational principle, and black hole partition functions. Lecture III: large and small BPS black holes in N=4 supergravity. Lecture IV: state counting for N=4 string compactifications. Appendix A: special geometry from the mathematical point of view. Appendix B: review of modular forms. Contains four problems which allow the readers to develop some of the key concepts by themselves.