Monday and Thursday 16:00­17:30, ESI, Boltzmann lecture hall
starting on October 30, 2006.

 
Supersymmetric black holes have been a major topic in string theory since the first microscopic derivation of the Bekenstein-Hawking entropy by A. Strominger and C. Vafa about ten years ago. More recently, the topic has attracted new interest through the work of H. Ooguri, A. Strominger and C. Vafa, who have proposed a relation between a black hole partition function and the partition function of the topological string. "Precision tests" of such proposals are possible since for supersymmetric black holes the relevant higher derivative terms in the effective action are under good control.

The objective of the lectures is to make these interesting new developments accessible to the participants (who are expected to have some initial knowledge of black holes in general relativity). The lectures will be divided into two parts. The first part, to be delivered in November 2006, will focus on the construction of black hole solutions in four-dimensional supergravity, including the effects of higher derivative terms in the action. The second part, taught in 2007, will review microscopic state counting and black hole partition functions.

A good fraction of the first part will be devoted to prepare the relevant material about black holes and supergravity, including the required elements of differential geometry. In particular, we will review Wald's definition of black hole entropy for gravitational actions with higher curvature terms, and the derivation of the zeroth and first law of black hole mechanics in this context. We will also explore the construction of the relevant supergravity actions using the superconformal calculus, and the so-called special geometry (of the field-dependent couplings) which tightly constrains them. Time permitting, we will explain in some detail how these tools have been used to construct supersymmetric black hole solutions for actions with higher derivative terms.