Oleg Lunin

Bubbling AdS space and 1/2 BPS geometries

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 AdS5 compactifications of M-theory preserving = 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.

Deforming field theories with U(1) × U(1) global symmetry and their gravity duals

We find the gravity dual of a marginal deformation of = 4 super Yang Mills, and discuss some of its properties. This deformation is intimately connected with an SL(2,) symmetry of the gravity theory. The SL(2,) 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.

AdS / CFT duality and the black hole information paradox

Abstract 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 .

Metric of the multiply wound rotating string

Abstract 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.

CORRELATION FUNCTIONS FOR MN/SN ORBIFOLDS

Abstract: We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds MN/SN, 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 N – this is a manifestation of the stringy exclusion principle.

Three-Point Functions for MN/SN Orbifolds¶with?= 4 Supersymmetry

Abstract: The D1–D5 system is believed to have an “orbifold point” in its moduli space where its low energy theory is a ?=4 supersymmetric sigma model with target space MN/SN, where M is T4 or K3. We study correlation functions of chiral operators in CFTs arising from such a theory. We construct a basic class of chiral operators from twist fields of the symmetric group and the generators of the superconformal algebra. We find explicitly the 3-point functions for these chiral fields at large N; these expressions are “universal” in that they are independent of the choice of M. We observe that the result is a significantly simpler expression than the corresponding expression for the bosonic theory based on the same orbifold target space.

What is the gravity dual of a chiral primary

Abstract In the AdS/CFT correspondence a chiral primary is described by a string theory solution with mass equaling angular momentum. For AdS 3 × S 3 we are led to consider three special families of metrics with this property: metrics with conical defects, Aichelburg–Sexl type metrics generated by rotating particles, and metrics generated by giant gravitons. We find that the first two of these are special cases of the complete family of chiral primary metrics which can be written down using the general solution in hep-th/0109154 , but they correspond to two extreme limits—the conical defect metrics map to CFT states generated by twist operators that are all identical, while the Aichelburg–Sexl metrics yield a wide dispersion in the orders of these twists. The giant graviton solutions in contrast do not represent configurations of the D1–D5 bound state; they correspond to fragmenting this system into two or more pieces. We look at the large distance behavior of the supergravity fields and observe that the excitation of these fields is linked to the existence of dispersion in the orders and spins of the twist operators creating the chiral primary in the CFT.

Black strings in asymptotically plane wave geometries

We present a class of black string spacetimes which asymptote to maximally symmetric plane wave geometries. Our construction will rely on a solution generating technique, the null Melvin twist, which deforms an asymptotically flat black string spacetime to an asymptotically plane wave black string spacetime while preserving the event horizon.

Rotating deformations of AdS3×S3, the orbifold CFT and strings in the pp-wave limit

Abstract We construct an exact metric which at short distances is the metric of massless particles in 5+1 spacetime (moving along a diameter of the sphere) and is AdS 3 × S 3 at infinity. We also consider a set of a conical defect spacetimes which are locally AdS 3 × S 3 and have the masses and charges of a special set of chiral primaries of the dual orbifold CFT. We find that excitation energies for a scalar field in the latter geometries agree exactly with the excitations in the corresponding CFT state created by twist operators: redshift in the geometry reproduces ‘long circle’ physics in the CFT. We propose a map of string states in AdS 3 × S 3 × T 4 to states in the orbifold CFT, analogous to the recently discovered map for AdS 5 × S 5 . The vibrations of the string can be pictured as oscillations of a Fermi sea in the CFT.

The slowly rotating near extremal D1–D5 system as a ‘hot tube’

Abstract The geometry of the D1–D5 system with a small angular momentum j has a long throat ending in a conical defect. We solve the scalar wave equation for low energy quanta in this geometry. The quantum is found to reflect off the end of the throat, and stay trapped in the throat for a long time. The length of the throat for j =1/2 equals n 1 n 5 R , the length of the effective string in the CFT; we also find that at this distance the incident wave becomes nonlinear. Filling the throat with several quanta gives a ‘hot tube’ which has emission properties similar to those of the near extremal black hole.