New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators

TL;DR

This paper introduces new recursion relations for AdS/CFT correlators that work in all dimensions and presents a method to extract flat-space S-matrix elements from these correlators, applicable even at loop level.

Contribution

The paper develops recursion relations for AdS/CFT correlators valid in all dimensions and introduces a novel technique to derive flat-space S-matrix elements from AdS/CFT data.

Findings

Recursion relations applicable in all dimensions including d=3.

Method to extract flat-space amplitudes from AdS/CFT correlators.

Recursion relations produce correlators with correct flat-space singularities.

Abstract

We consider correlation functions of the stress-tensor or a conserved current in AdS_{d+1}/CFT_d computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree level. These relations have an advantage over the BCFW-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including d=3. We also introduce a new method of extracting flat-space S-matrix elements from AdS/CFT correlators in momentum space. We show that the (d+1)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the d-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon or graviton amplitude appears as its coefficient.