26 - String black holes in four and five dimensions

Summary

Following our general plan, in Chapter 25 we have started to see classical solutions that describe the long-range fields generated by configurations of extended objects in string/M theory. In general, the solutions do not reflect some of the characteristics of the brane configuration which may be understood as “hair”, but in many cases of interest (in general, in the presence of unbroken supersymmetry), given a classical supergravity solution, we can tell which brane configurations give rise to it. This is in itself a very interesting development, but there is more, because, if the brane configurations only involve D-branes, they can be associated with two-dimensional CFTs (string theories) over which we have good control. Furthermore, each of the branes considered here (D- or not D-) has a worldvolume supersymmetric field theory associated with it. All this allows us to relate supergravity configurations to QFTs whose degrees of freedom can be understood as the microscopical degrees of freedom of the quantum (super)gravity theory contained in string/M theory. This is, roughly speaking, the basis of the AdS/CFT correspondence and generalizations [921, 234] and also the basis for the microscopical computations of BH entropies [1160], the subject of this chapter.

In this chapter we are going to present N = 2A/B, d = 10 SUEGRA solutions associated with configurations of extended objects of type-II superstring theories that lead to BH solutions of maximal d = 5, 4 SUEGRAs (N = 4, d = 5 and N = 8, d = 4) (Section 26.2) upon toroidal compactification. The association can be understood as a strong-weak-coupling limit (see Fig. 26.1). We will carefully relate the solutions' integration constants to the physical parameters of the stringy sources and then, using our knowledge of the QFTs associated with those sources in the extreme and supersymmetric cases, we will count the states of these QFTs at each energy level, and the corresponding entropy will be shown to coincide with one quarter of the area of the BH's horizon (Section 26.3).