We compute the properties of a class of charged black holes in anti-de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals-Maxwell liquid-gas system. In that case, the phases are controlled by the universal ''cusp'' and ''swallowtail'' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes. ͓S0556-2821͑99͒02316-4͔

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter spacetimes. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions dр7. As the counterterms eliminate the need of ''background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was ambiguous or unknown: topological black holes, Taub-NUTAdS and Taub-Bolt-AdS. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature. ͓S0556-2821͑99͒07318-X͔

The physical properties of Reissner-Nordström black holes in (nϩ1)-dimensional anti-de Sitter spacetime are related, by a holographic map, to the physics of a class of n-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes ͑in the canonical ensemble͒ and that of the van der Waals-Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific heats and electrical permittivity of the holes, and consider the analogue of the Clayperon equation at the phase boundaries. Consequently, we refine the phase diagrams in the canonical and grand canonical ensembles. We study the interesting physics in the neighborhood of the critical point in the canonical ensemble. There is a second order phase transition found there, and that region is characterized by a Landau-Ginzburg model with A 3 potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations.

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.