Three-point function in perturbed Liouville gravity

Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the one recently proposed in [G. Giribet, Nucl. Phys. B 737 (2006) 209] to describe the string theory in AdS3 space. Consequently, this computation extends previous results which presented free field calculations of particular cases of string amplitudes, and confirms that the free field approach leads to the exact result. Remarkably, this representation allows to compute winding violating three-point functions without making use of the spectral flow operator.Facultad de Ciencias Exacta

On spectral flow symmetry and Knizhnik-Zamolodchikov equation

It is well known that five-point function in Liouville field theory provides a representation of solutions of the SL (2, R) k Knizhnik–Zamolodchikov equation at the level of four-point function. Here, we make use of such representation to study some aspects of the spectral flow symmetry of sl ˆ (2) k affine algebra and its action on the observables of the WZNW theory. To illustrate the usefulness of this method we rederive the three-point function that violates the winding number in SL (2, R) in a very succinct way. In addition, we prove several identities holding between exact solutions of the Knizhnik–Zamolodchikov equation.Instituto de Física La Plat

Three-point function in perturbed Liouville gravity

Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the one recently proposed in [G. Giribet, Nucl. Phys. B 737 (2006) 209] to describe the string theory in AdS3 space. Consequently, this computation extends previous results which presented free field calculations of particular cases of string amplitudes, and confirms that the free field approach leads to the exact result. Remarkably, this representation allows to compute winding violating three-point functions without making use of the spectral flow operator.Facultad de Ciencias Exacta

The Stoyanovsky–Ribault–Teschner map and string scattering amplitudes

Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL(2,ℂ)k/SU(2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFT's as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formula connecting such amplitudes with observables in Liouville field theory. Finally, we study the WZNW correlation functions in the limit k → 0 and show that, at the point k = 0, the Stoyanovsky–Ribault–Teschner dictionary turns out to be in agreement with the FZZ conjecture at a particular point of the space of parameters where the Liouville central charge becomes cL = -2. This result makes contact with recent studies on the dynamical tachyon condensation in closed string theory.Facultad de Ciencias Exacta

Hairy black holes sourced by a conformally coupled scalar field in D dimensions

There exist well-known no-hair theorems forbidding the existence of hairy black hole solutions in general relativity coupled to a scalar conformal field theory in asymptotically flat space. Even in the presence of cosmological constant, where no-hair theorems can usually be circumvented and black holes with conformal scalar hair were shown to exist in D ≤ 4 dimensions, no-go results were reported for D > 4 . In this paper we prove that these obstructions can be evaded and we answer in the affirmative a question that remained open: Whether hairy black holes do exist in general relativity sourced by a conformally coupled scalar field in arbitrary dimensions. We find the analytic black hole solution in arbitrary dimension D > 4 , which exhibits a backreacting scalar hair that is regular everywhere outside and on the horizon. The metric asymptotes to (anti-)de Sitter spacetime at large distance and admits spherical horizon as well as horizon of a different topology. We also find analytic solutions when higher-curvature corrections O ( R n ) of arbitrary order n are included in the gravity action.Instituto de Física La Plat

Vacua of exotic massive 3D gravity

We consider the recently proposed exotic 3D massive gravity. We show that this theory has a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying either the standard Brown-Henneaux boundary conditions or the weakened asymptotic behavior of the so-called Log-gravity. Both sectors contain non-Einstein spaces with SO(2) × ℝ isometry group, showing that the Birkhoff theorem does not hold all over the parameter space, even if strong AdS boundary conditions are imposed. Some of these geometries correspond to 3D black holes dressed with a Log-gravity graviton. We conjecture that such geometries appear in a curve of the parameter space where the exotic 3D massive gravity on AdS3 is dual to a chiral conformal field theory. The theory also contains other interesting vacua, including different families of non-AdS black holes.Instituto de Física La Plat

Simple compactifications and black p-branes in Gauss-Bonnet and Lovelock theories

We look for the existence of asymptotically flat simple compactifications of the form D-p × T p in D-dimensional gravity theories with higher powers of the curvature. Assuming the manifold D-p to be spherically symmetric, it is shown that the Einstein-Gauss-Bonnet theory admits this class of solutions only for the pure Einstein-Hilbert or Gauss-Bonnet Lagrangians, but not for an arbitrary linear combination of them. Once these special cases have been selected, the requirement of spherical symmetry is no longer relevant since actually any solution of the pure Einstein or pure Gauss-Bonnet theories can then be toroidally extended to higher dimensions. Depending on p and the spacetime dimension, the metric on D-p may describe a black hole or a spacetime with a conical singularity, so that the whole spacetime describes a black or a cosmic p-brane, respectively. For the purely Gauss-Bonnet theory it is shown that, if D-p is four-dimensional, a new exotic class of black hole solutions exists, for which spherical symmetry can be relaxed. Under the same assumptions, it is also shown that simple compactifications acquire a similar structure for a wide class of theories among the Lovelock family which accepts this toroidal extension. The thermodynamics of black p-branes is also discussed, and it is shown that a thermodynamical analogue of the Gregory-Laflamme transition always occurs regardless the spacetime dimension or the theory considered, hence not only for General Relativity. Relaxing the asymptotically flat behavior, it is also shown that exact black brane solutions exist within a very special class of Lovelock theories.Instituto de Física La Plat