Subleading eikonal, AdS/CFT and double stress tensors

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Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-stress tensor operators to a heavyheavy-light-light correlator in a CFT of any even dimensionality with a large central charge.An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for any minimal-twist determines that for the higher minimal-twist and so on. To illustrate this procedure in four spacetime dimensions we determine the contributions of double-and triple-stress tensors.We compute the OPE coefficients; whenever results are available in the literature, we observe complete agreement. We also compute the contributions of double-stress tensors in six spacetime dimensions and determine the corresponding OPE coefficients. In all cases the results are consistent with the exponentiation of the near lightcone correlator. This is similar to the situation in two spacetime dimensions for the Virasoro vacuum block. September 2019karlsson, manuela, parnachev, tadicp @ maths.tcd.ie

Section: Twist-four Double-stress Tensorssupporting

confidence: 71%

Section: The Heavy-heavy-light-light Virasoro Vacuum Block Exponentiatesmentioning

confidence: 99%

“…Below we review the setup of a heavy-heavy-light-light correlator with focus on its behaviour in the lightcone limit. We mostly follow [30,41,32].…”

Section: Review Of Heavy-heavy-light-light Correlator In the Lightconmentioning

confidence: 99%

“…This can be written in terms of f 3 3 , Note that for ∆ L → ∞, the correlator is determined by the exponentiation of the stress tensor discussed e.g. in [32], i.e.…”

Section: (318)mentioning

confidence: 99%

Section: Ope Coefficients Of Triple-stress Tensorsmentioning

confidence: 99%

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Leading multi-stress tensors and conformal bootstrap

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Notes on AdS-Schwarzschild eikonal phase

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2021

We consider the eikonal phase associated with the gravitational scattering of a highly energetic light particle off a very heavy object in AdS spacetime. A simple expression for this phase follows from the WKB approximation to the scattering amplitude and has been computed to all orders in the ratio of the impact parameter to the Schwarzschild radius of the heavy particle. The eikonal phase is related to the deflection angle by the usual stationary phase relation. We consider the flat space limit and observe that for sufficiently small impact parameters (or angular momenta) the eikonal phase develops a large imaginary part; the inelastic cross-section is exactly the classical absorption cross-section of the black hole. We also consider a double scaling limit where the momentum becomes null simultaneously with the asymptotically AdS black hole becoming very large. In the dual CFT this limit retains contributions from all leading twist multi stress tensor operators, which are universal with respect to the addition of higher derivative terms to the gravitational lagrangian. We compute the eikonal phase and the associated Lyapunov exponent in the double scaling limit.