Low-energy, near-horizon scaling limits of black holes which lead to string theory on AdS 2 × S 2 are described. Unlike the higher-dimensional cases, in the simplest approach all finite-energy excitations of AdS 2 ×S 2 are suppressed. Surviving zero-energy configurations are described. These can include tree-like structures in which the AdS 2 ×S 2 throat branches as the horizon is approached, as well as disconnected AdS 2 × S 2 universes. In principle, the black hole entropy counts the quantum ground states on the moduli space of such configurations. In a nonsupersymmetric context AdS D for general D can be unstable against instanton-mediated fragmentation into disconnected universes. Several examples are given.

Type IIB strings are compactified on a Calabi-Yau three-fold. When Calabi-Yau-valued expectation values are given to the NS-NS and RR three-form field strengths, the dilaton hypermultiplet becomes both electrically and magnetically charged. The resultant classical potential is calculated, and minima are found. At singular points in the moduli space, such as Argyres-Douglas points, supersymmetric minima are found. A formula for the classical potential in N = 2 supergravity is given which holds in the presence of both electric and magnetic charges.

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We construct a family of solutions in IIB supergravity theory. These are time dependent or depend on a light-like coordinate and can be thought of as deformations of AdS 5 × S 5 . Several of the solutions have singularities. The light-like solutions preserve 8 supersymmetries. We argue that these solutions are dual to the N = 4 gauge theory in a 3 + 1 dimensional spacetime with a metric and a gauge coupling that is varying with time or the light-like direction respectively. This identification allows us to map the question of singularity resolution to the dual gauge theory.

The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional N = 1 supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit is found in which the dynamics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This decoupling suggests that the quantum states supported in the near-horizon moduli space can be interpreted as internal states of a single composite black hole carrying all of the charge. The near-horizon theory is shown to have an enhanced D(2, 1; 0) superconformal symmetry. Eigenstates of the Hamiltonian H of the near-horizon theory are ill-defined due to noncompact regions of the moduli space corresponding to highly redshifted near-coincident black holes. It is argued that one should consider, instead of H eigenstates, eigenstates of 2L 0 = H + K, where K is the generator of special conformal transformations. The result is a well defined Hilbert space with a discrete spectrum describing the N-black hole dynamics.