Subleading Eikonal, AdS/CFT and Double Stress Tensors

TL;DR

This work studies the subleading eikonal phase in AdS/CFT as encoded in heavy-heavy-light-light correlators in a holographic CFT. The authors derive a closed-form OPE for leading-twist double-stress-tensor operators in 4d, then perform an exact sum over these operators to obtain the O(mu^2) lightcone behavior of the HHLL four-point function. The resulting expression, written in a compact form with hypergeometric functions, passes nontrivial checks, including agreement with the Regge limit at large impact parameter and consistency when analyzed in the S-channel. The results support the idea that subleading gravitational effects in AdS are captured by the squared stress-tensor sector in the CFT and point toward a universal structure for higher-dimensional heavy-light correlators and higher-order eikonal terms.

Abstract

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. We provide a closed form expression for the OPE coefficients 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.