We obtain a new class of spinning charged extremal black holes in five dimensions, considered both as classical configurations and in the Dirichlet(D)-brane representation. The degeneracy of states is computed from the D-brane side and the entropy agrees perfectly with that obtained from the black hole side. 2/96♣

We consider slightly nonextremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees, up to a mysterious factor, with an entropy derived by counting non-BPS excitations of the Dirichlet 3-brane. These excitations are described in terms of the statistical mechanics of a ͑3ϩ1͒dimensional gas of massless open string states. This is essentially the classic problem of blackbody radiation. The blackbody temperature is related to the temperature of the Hawking radiation. We also construct a solution of type IIB supergravity describing a 3-brane with a finite density of longitudinal momentum. For extremal momentum-carrying 3-branes the horizon area vanishes. This is in agreement with the fact that the BPS entropy of the momentum-carrying Dirichlet 3-branes is not an extensive quantity. ͓S0556-2821͑96͒00218-4͔Working out the precise normalizations, we find that the Bekenstein-Hawking and statistical entropies are not identical, but are related by a mysterious proportionality factor. If, however, only the transverse excitation modes of the 3-brane are counted, then the statistical entropy becomes identical to *Electronic address: ssgubser@puhep1.princeton.edu † Electronic address: klebanov@puhep1.princeton.edu ‡ Electronic address: peet@viper.princeton.edu 1 In this short article we will not attempt to refer to all of the developments in the recent black hole literature.

In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. The corresponding bounds in case of Schwarzschild (M ≥ 0 ) and Reissner-Nordström (M ≥ |q|) black holes are known to coincide with the requirement that naked singularities be absent.Here we investigate (U(1)) 2 charged dilaton black holes in this context. The extreme solutions are shown to saturate the supersymmetry bound of N = 4 d = 4 supergravity, or dimensionally reduced superstring theory. Specifically, we have shown that extreme dilaton black holes, with electric and magnetic charges, admit supercovariantly constant spinors. The supersymmetric positivity bound for dilaton black holes, M ≥ 1 √ 2 (|Q|+|P |), takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition.The temperature, entropy and singularity of the stringy black hole are discussed in connection with the extreme limit and restoration of supersymmetry. The Euclidean action (entropy) of the extreme black hole is given by 2π|P Q|. We argue that this result is not altered by higher order corrections in the supersymmetric theory. In Lorentzian signature, quantum corrections to the effective on-shell action in the extreme black hole background are also absent.When a black hole reaches its extreme limit, the thermal description breaks down. It cannot continue to evaporate by emitting (uncharged) elementary particles, since this would violate the supersymmetric positivity bound. We speculate on the possibility that an extreme black hole may "evaporate" by emitting smaller extreme black holes.1 On leave from: Lebedev Physical Institute, Moscow. Bitnet address: kallosh@slacvm 2 On leave from: Lebedev Physical Institute,

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.1 Understanding the physics of spacetime singularities is a challenge for any complete theory of quantum gravity. It has been shown that string theory resolves certain seeming singularities, such as orbifolds [1], flops [2], and conifolds [3], in the sense that their physics is completely nonsingular. On the other hand, it has also been argued that certain singularities should not be resolved, but rather must be disallowed configurations -in particular, negative mass Schwarzschild, which would correspond to an instability of the vacuum [4]. Also, in the study of perturbations of the AdS/CFT duality various singular spacetimes have been encountered, and at least some of these must be unphysical in the same sense as negative mass Schwarzschild. A more general understanding of singularities in string theory is thus an important goal.In this paper we study a naked singularity of a particular type [5,6,7], which has been dubbed the repulson. A variety of brane configurations in string theory appear to give rise to such a singularity. However, we will argue that this is not the case. Rather, as the name might suggest, the constituent branes effectively repel one another (in spite of supersymmetry), forming in the end a nonsingular shell.Our interest in this singularity arose from a search for new examples of gauge/gravity duality. In particular, the brane configurations that give rise to the repulson singularity have on their world-volumes pure D = 4, N = 2 gauge theory (or the equivalent in other dimensions), as opposed to the usual pure D = 4, N = 4, or D = 4, N = 2 with hypermultiplets. We do not precisely find such a duality, in the sense of using supergravity to calculate properties of the strongly coupled gauge theory, but we do find a striking parallel between the moduli space of the large-N SU(N) gauge theory and the fate that we have deduced for the singularity. We also find some clues which allow us to guess at aspects of a possible dual.

We point out that two distinct distance-energy relations have been discussed in the AdS/CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe processes, the holographic principle, and black hole entropies.