How to Count the States of Extremal Black Holes in N = 8 Supergravity

Abstract

The basic technique for counting the states of extremal black holes in string theory is to represent the black hole as a bound state of p-brane solitons. The horizon area of the resulting supergravity solution is related to an entropy by the Bekenstein-Hawking formula S = A/4G N . At weak coupling, p-branes charged under the Ramond-Ramond fields of Type II string theory are easily quantized as D-branes [1]. This fact was exploited in the seminal paper of Strominger and Vafa who showed that for some black holes corresponding at weak coupling to systems of D-branes, the collective coordinate degeneracy of the bound state can be easily calculated [2]. If the bound state in question is a BPS state, this degeneracy can be extrapolated back to strong coupling since the representation theory of supersymmetry protects it from corrections. To summarize, the program for counting the states of black holes amounts to treating the black hole as a bound state of solitons, quantizing the solitons at weak coupling, and extrapolating the resulting collective coordinate degeneracy back to strong coupling via an appeal to supersymmetry.