AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence

The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights obtained in this direction over the last decade and apply the new techniques to Topologically Massive Gravity. We show that this theory is dual to a non-unitary CFT for any value of its parameter mu and becomes a Logarithmic CFT at mu = 1.Comment: 10 pages, proceedings for XXV Max Born Symposium, talks given at Johns Hopkins workshop and Holographic Cosmology workshop at Perimeter Institute; v2: added reference

Real-time gauge/gravity duality and ingoing boundary conditions

In arXiv:0805.0150 [hep-th] and arXiv:0812.2909 [hep-th] a general prescription was presented for the computation of real-time correlation functions using the gauge/gravity duality. I apply this prescription to the specific case of retarded thermal correlation functions and derive the usual ingoing boundary conditions at the horizon for bulk fields. The derivation allows me to clarify various issues, in particular the generalization to higher-point functions and the relevance of including the regions beyond the horizon.Comment: 5 pages, 2 figures; expanded version of contribution to the Cargese 2008 proceeding

The S-matrix bootstrap. Part I : QFT in AdS.

We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques

QFT in AdS instead of LSZ

The boundary correlation functions for a QFT in a fixed AdS background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptions we rigorously show that the resulting S-matrix element obeys a dispersion relation, the non-linear unitarity conditions, and the Froissart-Martin bound. QFT in AdS thus provides an alternative route to fundamental QFT results that normally rely on the LSZ axioms.Comment: 8 pages, 1 figur

Flat-space Partial Waves From Conformal OPE Densities

We consider the behavior of the OPE density $c(\Delta,\ell)$ for conformal four-point functions in the flat-space limit where all scaling dimensions become large. We find evidence that the density reduces to the partial waves $f_\ell(s)$ of the corresponding scattering amplitude. The Euclidean inversion formula then reduces to the partial wave projection and the Lorentzian inversion formula to the Froissart-Gribov formula. The flat-space limit of the OPE density can however also diverge, and we delineate the domain in the complex $s$ plane where this happens. Finally we argue that the conformal dispersion relation reduces to an ordinary single-variable dispersion relation for scattering amplitudes.Comment: 39 pages + appendices, 13 figures; v2: references adde

Applications of alpha space

We extend the definition of ‘alpha space’ as introduced in [1] to two spacetime dimensions. We discuss how this can be used to find conformal block decompositions of known functions and how to easily recover several lightcone bootstrap results. In the second part of the paper we establish a connection between alpha space and the Lorentzian inversion formula of [2]