Abstract
Highly energetic particles traveling in the background of an asymptotically AdS black hole experience a Shapiro time delay and an angle deflection. These quantities are related to the Regge limit of a heavy-heavy-light-light four-point function of scalar operators in the dual CFT. The Schwarzschild radius of the black hole in AdS units is proportional to the ratio of the conformal dimension of the heavy operator and the central charge. This ratio serves as a useful expansion parameter; its power counts the number of stress tensors in the multi-stress tensor operators which contribute to the four-point function. In the cross-channel the four-point function is determined by the OPE coefficients and anomalous dimensions of the heavy-light double-trace operators. We explain how this data can be obtained and explicitly compute the first and second order terms in the expansion of the anomalous dimensions. We observe perfect agreement with known results in the lightcone limit, which were obtained by computing perturbative corrections to the energy eigenstates in AdS spacetimes.
Highlights
Introduction and summary1.1 IntroductionThe AdS/CFT correspondence provides a non-perturbative definition of quantum gravity in negatively curved spacetimes [1,2,3]
In this paper we explain how to compute the anomalous dimensions of heavy-light doubletrace operators [OH OL]n,l order by order in μ, using the phase shift result of [71]
We show that the O(μ2) anomalous dimensions in any d are given by γ (2)
Summary
Introduction and summary1.1 IntroductionThe AdS/CFT correspondence provides a non-perturbative definition of quantum gravity in negatively curved spacetimes [1,2,3]. The correspondence in principle provides an opportunity to study generic properties of quantum gravity, possibly probing regimes unattainable by low-energy effective theories. Crossing symmetry in CFTs imposes highly non-trivial constraints on the theory. The idea of conformal bootstrap is to use these constraints to put restrictions on the CFT data or, if possible, even solve the theory. One way to make use of the crossing symmetry is to isolate a small number of contributing operators in one channel, e.g. by going to a certain kinematical regime. This typically has to be reproduced by the exchange of an infinite number of operators in another channel. The Regge limit provides another opportunity to isolate the contribution of a class of operators, those of highest spin
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