We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future) horizon. The solutions are naturally embedded in string and M-theory. In the particular case of a two-dimensional cosmology, space-time is flat with an identification under boost and translation transformations. We consider the corresponding string theory orbifold and calculate the modular invariant one-loop partition function. In this case there is a strong parallel with the BTZ black hole. The higher dimensional cosmologies have a time-like curvature singularity in the intermediate region. In some cases the string coupling can be made small throughout all of space-time but string corrections become important at the singularity. This happens where string winding modes become light which could resolve the singularity. The new proposed space-time causal structure could have implications for cosmology, independently of string theory.

Abstract:We introduce the impact parameter representation for conformal field theory correlators of the form A ∼ O 1 O 2 O 1 O 2 . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function O 1 O 1 shock in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch cut, we find the high spin and dimension conformal partial wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T -channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high spin O 1 O 2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ∼ O 1 O 1 shock in the presence of a shock wave in Anti-de Sitter, where O 1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ∼ O 1 O 2 O 1 O 2 , where O 2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

We investigate the deformation of D-brane world-volumes in curved backgrounds. We calculate the leading corrections to the boundary conformal field theory involving the background fields, and in particular we study the correlation functions of the resulting system. This allows us to obtain the world-volume deformation, identifying the open string metric and the noncommutative deformation parameter. The picture that unfolds is the following: when the gauge invariant combination ω = B + F is constant one obtains the standard Moyal deformation of the brane world-volume. Similarly, when dω = 0 one obtains the noncommutative Kontsevich deformation, physically corresponding to a curved brane in a flat background. When the background is curved, H = dω = 0, we find that the relevant algebraic structure is still based on the Kontsevich expansion, which now defines a nonassociative star product with an A ∞ homotopy associative algebraic structure. We then recover, within this formalism, some known results of Matrix theory in curved backgrounds. In particular, we show how the effective action obtained in this framework describes, as expected, the dielectric effect of D-branes. The polarized branes are interpreted as a soliton, associated to the condensation of the brane gauge field.Noncommutative quantum field theoretic limits of string theory have received considerable attention in the recent literature, and have been studied in a variety of papers (see, e.g., [1,2,3,4,5,6] and references therein). The attention is focused on a specific scaling limit, where the effects of large magnetic backgrounds are translated into Moyal noncommutative deformations of the D-brane world-volume algebra of functions. The open string physics is therefore captured within a quantum field theory (which is renormalizable, despite appearances [7,8]). A common point to most previous investigations is that the background (sigma model) fields are taken to be constant and that, as a consequence, the target space is flat. One may then ask the natural question of what happens if the background is curved, i.e., if the background fields are no longer constant? This question received some attention in a couple of recent papers [9,10,11,12], but there is no general answer to it (other papers of interest with some relation to this subject are, e.g., [13,14,15,16]). Our goal in this work is to address this problem in the context of a simple model with weakly curved backgrounds, which can be on one side connected to the known flat background framework, and on the other hand can be related to formal results of brane physics in WZW models, which can be analyzed exactly with conformal field theory techniques [10,11,17].More concretely, the aim of this paper is to understand how the presence of a nontrivial background field affects the world-volume deformation of a D-brane. It is known that, in the presence of a constant background B-field, the physics can be exactly described either by a sigma model approach [18,19,20,21,22,23,24,25], or alternatively, by trans...

We derive an eikonal approximation to high energy interactions in Anti-de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space. We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual conformal field theory four-point function O 1 O 2 O 1 O 2 for small values of the cross ratios, in a Lorentzian regime. Finally we show that the phase shift is dominated by graviton exchange and computes, in the dual CFT, the anomalous dimension of the double trace primary operators O 1 ∂ · · · ∂O 2 of large dimension and spin, corresponding to the relative motion of the two interacting particles. The results are valid at strong t'Hooft coupling and are exact in the 1/N expansion.