Near Horizon Limits of Massless BTZ and Their CFT Duals

We consider the massless BTZ black hole and show that it is possible to take its "near horizon" limit in two distinct ways. The first one leads to a null self-dual orbifold of AdS3 and the second to a spacelike singular AdS3/Z_K orbifold in the large K limit, the "pinching orbifold". We show that from the dual 2d CFT viewpoint, the null orbifold corresponds to the p^+=0 sector of the Discrete Light-Cone Quantisation (DLCQ) of the 2d CFT where a chiral sector of the CFT is decoupled, while the pinching orbifold corresponds to taking an infinite mass gap limit in both the right and left sectors of the 2d CFT, essentially leaving us with the states L_0=\bar L_0=c/24 only. In the latter case, one can combine the near horizon limit with sending the 3d Planck length l_P to zero, or equivalently the dual CFT central charge c to infinity. We provide preliminary evidence that in that case some nontrivial dynamics may survive the limit.Comment: 22 pages, no figures, v2: minor improvements, references adde

From de Sitter to de Sitter

We obtain D=6, N=(1,1) de Sitter supergravity from a hyperbolic reduction of the massive type IIA* theory. We construct a smooth cosmological solution in which the co-moving time runs from an infinite past, which is dS_4\times S^2, to an infinite future, which is a dS_6-type spacetime with the boundary R^3\times S^2. This provides an effective four-dimensional cosmological model with two compact extra dimensions forming an S^2. Interestingly enough, although the solution is time-dependent, it arises from a first-order system via a superpotential construction. We lift the solutions back to D=10, and in particular obtain two smooth embeddings of dS_4 in massive type IIA*, with the internal space being either H^4\times S^2 or an H^4 bundle over S^2. We also obtain the analogous D=5 and D=4 solutions. We show that there exist cosmological solutions that describe an expanding universe with the expansion rate significantly larger in the past than in the future.Comment: Latex three times, 22 pages, references adde

Constraining conformal field theories with a slightly broken higher spin symmetry

We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual large N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one gets in the Vasiliev theories. Namely, the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of order 1/N. Using the slightly broken higher spin symmetry we constrain the three point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points we get the critical O(N) models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Comment: 54 pages, 3 figure

Massless black holes and black rings as effective geometries of the D1-D5 system

We compute correlation functions in the AdS/CFT correspondence to study the emergence of effective spacetime geometries describing complex underlying microstates. The basic argument is that almost all microstates of fixed charges lie close to certain "typical" configurations. These give a universal response to generic probes, which is captured by an emergent geometry. The details of the microstates can only be observed by atypical probes. We compute two point functions in typical ground states of the Ramond sector of the D1-D5 CFT, and compare with bulk two-point functions computed in asymptotically AdS_3 geometries. For large central charge (which leads to a good semiclassical limit), and sufficiently small time separation, a typical Ramond ground state of vanishing R-charge has the M=0 BTZ black hole as its effective description. At large time separation this effective description breaks down. The CFT correlators we compute take over, and give a response whose details depend on the microstate. We also discuss typical states with nonzero R-charge, and argue that the effective geometry should be a singular black ring. Our results support the argument that a black hole geometry should be understood as an effective coarse-grained description that accurately describes the results of certain typical measurements, but breaks down in general.Comment: 47 pages, 4 figures. v2: references added. v3: minor corrections to Appendix A, references adde

Deformations of flows from type IIB supergravity

We consider supersymmetric SL(3,R) deformations of various type IIB supergravity backgrounds which exhibit flows away from an asymptotically locally AdS_5 x S^5 fixed point. This includes the gravity dual of the Coulomb branch of N=1 super Yang Mills theory, for which the deformed superpotential is known. We also consider the gravity duals of field theories which live on various curved backgrounds, such as Minkowski_2 x H^2, AdS_3 x S^1 and R x S^3. Some of the deformed theories flow from a four-dimensional N=1 superconformal UV fixed point to a two-dimensional (2,2) superconformal IR fixed point. We study nonsupersymmetric generalizations of the deformations of the above Coulomb branch flows.Comment: 29 pages, additional references and comment

Aspects of Quantum Gravity in de Sitter Spaces

In these lectures we give a review of recent attempts to understand quantum gravity on de Sitter spaces. In particular, we discuss the holographic correspondence between de Sitter gravity and conformal field theories proposed by Hull and by Strominger, and how this may be reconciled with the finite-dimensional Hilbert space proposal by Banks and Fischler. Furthermore we review the no-go theorems that forbid an embedding of de Sitter spaces in string theory, and discuss how they can be circumvented. Finally, some curious issues concerning the thermal nature of de Sitter space are elucidated.Comment: 36+1 pages, 5 Postscript figures, introduction and section 6 extended, further references, final version to appear in JCA

Non-extremal Black Holes, Harmonic Functions, and Attractor Equations

We present a method which allows to deform extremal black hole solutions into non-extremal solutions, for a large class of supersymmetric and non-supersymmetric Einstein-Vector-Scalar type theories. The deformation is shown to be largely independent of the details of the matter sector. While the line element is dressed with an additional harmonic function, the attractor equations for the scalars remain unmodified in suitable coordinates, and the values of the scalar fields on the outer and inner horizon are obtained from their fixed point values by making specific substitutions for the charges. For a subclass of models, which includes the five-dimensional STU-model, we find explicit solutions.Comment: 33 page

Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity

One would often like to know when two a priori distinct extremal black p-brane solutions are in fact U-duality related. In the classical supergravity limit the answer for a large class of theories has been known for some time. However, in the full quantum theory the U-duality group is broken to a discrete subgroup and the question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of N=8 supergravity in four, five and six dimensions. The purpose of this note is to present and clarify what is currently known about these discrete orbits while at the same time filling in some of the details not yet appearing in the literature. To this end we exploit the mathematical framework of integral Jordan algebras and Freudenthal triple systems. The charge vector of the dyonic black string in D=6 is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. The situation in four dimensions is less clear: while black holes preserving more than 1/8 of the supersymmetries may be fully classified by known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes a complete classification is known. All projective black holes are E_{7(7)}(Z) related to a four or five charge canonical form determined uniquely by the set of known arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to appear in Class. Quantum Gra

NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion

Using the algebraic geometric approach of Berenstein et {\it al} (hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with discrete torsion. We first develop a new way of getting complex $d$ mirror Calabi-Yau hypersurfaces $H_{\Delta}^{\ast d}$ in toric manifolds $M_{\Delta }^{\ast (d+1)}$ with a $C^{\ast r}$ action and analyze the general group of the discrete isometries of $H_{\Delta}^{\ast d}$. Then we build a general class of $d$ complex dimension NC mirror Calabi-Yau orbifolds where the non commutativity parameters $\theta_{\mu \nu}$ are solved in terms of discrete torsion and toric geometry data of $M_{\Delta}^{(d+1)}$ in which the original Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the NC algebra for generic $d$ dimensions NC Calabi-Yau manifolds and give various representations depending on different choices of the Calabi-Yau toric geometry data. We also study fractional D-branes at orbifold points. We refine and extend the result for NC $T^{2})/(\mathbf{{Z_{2}}\times {Z_{2})}}$ to higher dimensional torii orbifolds in terms of Clifford algebra.Comment: 38 pages, Late

Closed String Tachyon Condensation: An Overview

These notes are an expanded version of a review lecture on closed string tachyon condensation at the RTN workshop in Copenhagen in September 2003. We begin with a lightning review of open string tachyon condensation, and then proceed to review recent results on localized closed string tachyon condensation, focusing on two simple systems, C/Z_n orbifolds and twisted circle compactifications.Comment: harvmac, 59 pages; references adde