Monday and Thursday, 16:00-17:30, Schrödinger lecture hall
May 21 to June 14, 2006

 
The second part of the course concentrates on microscopic aspects of black hole physics. We first review the heuristic string - black hole correspondence introduced by L. Susskind. Then we study three examples where supersymmetry allows an asymptotically exact counting of microstates in string theory:
(i) electric BPS states of the heterotic string compactified on a six-torus. The state counting is equivalent to a version of the classical problem of counting the partions of a large integer solved by Hardy and Ramanujan. We use this case to explain the idea of the Rademacher expansion, which allows to compute the state degeneracy to arbitrary precision. The leading order approximation, corresponding to the Cardy formula well known to physicists, will be posed as a guided exercise for students.
(ii) dyonic BPS states of the heterotic string compactified on a six-torus. Here we review the counting formula of Dijkgraaf-Verlinde-Verlinde (DVV) and its relation to Siegel modular forms. The asymptotic evaluation of the DVV formula will be sketched.
(iii) BPS states of the M5-brane wrapped on a four-cycle within a Calabi-Yau threefold. This represents the most general type of supersymmetric black holes which can be handled quantitatively.

In the second half of the lectures we first explain how the black hole attractor equations and the black hole entropy can be derived from a variational principle based on an entropy function. This leads, following the work of Ooguri-Strominger-Vafa, to the introduction of black hole partition functions, which are intimately related to the topological string. We will give a critical review of this subject, mentioning both successful tests and open conceptual and technical questions.