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

TL;DR

<3-5 sentence high-level summary> This work provides explicit four-point functions for the stress tensor and conserved currents in AdS$_4$/CFT$_3$ by leveraging a momentum-space recursion that expresses the correlator as a sum over residues of a rational integrand built from deformed three-point transition amplitudes. The authors derive complete formulas for arbitrary external helicities, confirm that the flat-space limit reproduces the known four-dimensional MHV gluon and graviton amplitudes, and show that the correlators are rational in spinor variables with no boundary logarithms. The approach bypasses the complexity of direct Witten diagram evaluations and reveals a simple analytic structure in momentum space, with potential extensions to supersymmetric and higher-spin theories. These results provide a powerful framework for testing AdS/CFT at four points and for connecting AdS correlators to flat-space scattering data.

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.