Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3

TL;DR

This paper calculates four-point correlation functions of stress tensors and conserved currents in AdS_4/CFT_3, using recursion relations to simplify the process and revealing simple analytic structures in momentum space.

Contribution

It introduces a recursion-based method to compute four-point functions in AdS_4/CFT_3, avoiding complex Witten diagram evaluations and explicitly relating MHV amplitudes to correlator coefficients.

Findings

Recursion relations simplify four-point function calculations.

MHV amplitudes appear as specific singularities in correlators.

Results exhibit remarkably simple analytic structures in momentum space.

Abstract

We compute four point functions of the stress tensor and conserved currents in AdS_4/CFT_3 using bulk perturbation theory. We work at treel level in the bulk theory, which we take to be either pure gravity or Yang Mills theory in AdS. We bypass the tedious evaluation of Witten diagrams using recently developed recursion relations for these correlators. In this approach, the four point function is obtained as the sum of residues of a rational function at easily identifiable poles. We write down an explicit formula for the four point correlator with arbitrary external helicities and momenta. We verify that, precisely as conjectured in a companion paper, the Maximally Helicity Violating (MHV) amplitude of gravitons or gluons appears as the coefficient of a specified singularity in the MHV stress-tensor or current correlator. We comment on the remarkably simple analytic structure of our answers in momentum space.