Energy-Momentum Conservation and Holographic S-Matrix

TL;DR

This paper explores how energy-momentum conservation impacts the holographic S-matrix within AdS/CFT, revealing it isn't a direct consequence of conformal invariance and predicting a new singularity in correlation functions.

Contribution

It demonstrates that energy-momentum conservation does not naturally follow from conformal invariance in the large N limit and predicts a novel singularity in four-point correlation functions.

Findings

Energy-momentum conservation is not a natural consequence of conformal invariance.

A new singularity in the four-point correlation function of a marginal operator is predicted.

The two-point scattering amplitude calculated aligns with theoretical expectations.

Abstract

We investigate the consequence of the energy-momentum conservation law for the holographic S-matrix from AdS/CFT correspondence. It is shown that the conservation law is not a natural consequence of conformal invariance in the large N limit. We predict a new singularity for the four point correlation function of a marginal operator. Only the two point scattering amplitude is explicitly calculated, and the result agrees with what is expected.