We consider all 1/2 BPS excitations of AdS × S configurations in both type IIB string theory and M-theory. In the dual field theories these excitations are described by free fermions. Configurations which are dual to arbitrary droplets of free fermions in phase space correspond to smooth geometries with no horizons. In fact, the ten dimensional geometry contains a special two dimensional plane which can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the collection of droplets on this plane. These solutions also give a very explicit realization of the geometric transitions between branes and fluxes. We also describe all 1/2 BPS excitations of plane wave geometries. The problem of finding the explicit geometries is reduced to solving a Laplace (or Toda) equation with simple boundary conditions. We present a large class of explicit solutions. In addition, we are led to a rather general class of AdS 5 compactifications of M-theory preserving N = 2 superconformal symmetry. We also find smooth geometries that correspond to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, we present a smooth 1/2 BPS solution of seven dimensional gauged supergravity corresponding to a condensate of one of the charged scalars.

We find the gravity dual of a marginal deformation of N = 4 super Yang Mills, and discuss some of its properties. This deformation is intimately connected with an SL(2, R) symmetry of the gravity theory. The SL(2, R) transformation enables us to find the solutions in a simple way. These field theory deformations, sometimes called β deformations, can be viewed as arising from a star product. Our method works for any theory that has a gravity dual with a U(1) × U(1) global symmetry which is realized geometrically. These include the field theories that live on D3 branes at the conifold or other toric singularities, as well as their cascading versions.

Near-extremal black holes are obtained by exciting the Ramond sector of the D1-D5 CFT, where the ground state is highly degenerate. We find that the dual geometries for these ground states have throats that end in a way that is characterized by the CFT state. Below the black hole threshold we find a detailed agreement between propagation in the throat and excitations of the CFT. We study the breakdown of the semiclassical approximation and relate the results to the proposal of gr-qc/0007011 for resolving the information paradox: semiclassical evolution breaks down if hypersurfaces stretch too much during an evolution. We find that a volume V stretches to a maximum throat depth of V/2G.Comment: 57 pages, Latex, 9 figure

We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M N /S N , where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions. Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g. For large N, this genus expansion coincides with a 1/N expansion. The contribution from the covering space of genus zero is 'universal' in the sense that it depends only on the central charge of the CFT. For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions. The condition for the genus zero contribution to the 3-point functions to be non-vanishing is similar to the fusion rules for an SU(2) WZW model. We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of Nthis is a manifestation of the stringy exclusion principle.

We consider a string wrapped many times around a compact circle in space, and let this string carry a right moving wave which imparts momentum and angular momentum to the string. The angular momentum causes the strands of the `multiwound' string to separate and cover the surface of a torus. We compute the supergravity solution for this string configuration. We map this solution by dualities to the D1-D5 system with angular momentum that has been recently studied. We discuss how constructing this multiwound string solution may help us to relate the microscopic and macroscopic pictures of black hole absorption.Comment: 30 pages, references adde