Abstract
The eikonal phase which determines the Regge limit of the gravitational scat- tering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes of any dimensionality has been com- puted to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius. The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single stress tensor conformal block, but the subleading term is a result of an infinite sum of the double stress tensor contributions. We provide a closed form expression for the OPE coef- ficients of the leading twist double stress tensors in four spacetime dimensions and perform the sum to compute the corresponding lightcone behavior of a heavy-heavy-light-light CFT correlator. The resulting compact expression passes a few nontrivial independent checks. In particular, it agrees with the subleading eikonal phase at large impact parameter.
Highlights
The eikonal phase which determines the Regge limit of the gravitational scattering amplitude of a light particle off a heavy one in Minkowski spacetimes admits an expansion in the ratio of the Schwarzschild radius of the heavy particle to the impact parameter
Such an eikonal phase in AdS spacetimes of any dimensionality has been computed to all orders and reduces to the corresponding Minkowski result when both the impact parameter and the Schwarzschild radius are much smaller than the AdS radius
The leading term in the AdS eikonal phase can be reproduced in the dual CFT by a single stress tensor conformal block, but the subleading term is a result of an infinite sum of the double stress tensor contributions
Summary
A notable class of double-trace operators in this context concerns those constructed from the stress tensor, with dimension ∆n,s = 4 + 2n + s, spin s and twist ∆n,s − s = 4 + 2n (to leading order in 1/CT ):. It is very easy to check that these equations are consistent with the OPE coefficients computed in [45] for a few double stress tensor operators of low spin. The first non-trivial check of eq (1.10) involves taking the large impact parameter regime of the Regge limit This reproduces the corresponding expression obtained earlier in [41]. Which can be exactly matched to the respective limit of the correlator computed in the crossing channel, provided O(μ2) anomalous dimensions of certain heavy-light double trace operators.
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