Black Hole Microstate Counting and its Macroscopic Counterpart

We survey recent results on the exact dyon spectrum in a class of N=4 supersymmetric string theories, and discuss how the results can be understood from the macroscopic viewpoint using AdS2/CFT1 correspondence. The comparison between the microscopic and the macroscopic results includes power suppressed corrections to the entropy, the sign of the index, logarithmic corrections and also the twisted index measuring the distribution of discrete quantum numbers among the microstates.(Based on lectures given by A.S. at the 12th Marcel Grossmann Meeting On General Relativity, 12–18 Jul 2009, Paris, France; CERN Winter School on Supergravity, Strings, and Gauge Theory, 25–29 January 2010; String Theory: Formal Developments And Applications, 21 Jun – 3 Jul 2010, Cargese, France, and notes taken by I.M. at the Cargese school.)