Towards S matrices on flat space and pp waves from SYM

TL;DR

This paper explores methods to derive S matrices for flat space and pp waves from SYM correlators, addressing subtleties and limitations, and comparing results with AdS calculations.

Contribution

It introduces a generalized procedure to extract S matrices from SYM correlators for flat space and pp waves, including analysis of extremal correlators.

Findings

Only extremal correlators survive the pp wave limit

SYM and AdS results match in angular dependence for extremal 3-point functions

Energy dependence of S matrices differs between SYM and AdS calculations

Abstract

We analyze the possibility of extracting S matrices on pp waves and flat space from SYM correlators. For pp waves, there is a subtlety in defining S matrices, but we can certainly obtain observables. Only extremal correlators survive the pp wave limit. A first quantized string approach is inconclusive, producing in the simplest form results that vanish in the pp wave limit. We define a procedure to get S matrices from SYM correlators, both for flat space and for pp waves, generalizing a procedure due to Giddings. We analyze nonrenormalized correlators: 2 and 3 -point functions and extremal correlators. For the extremal 3-point function, the SYM and AdS results for the S matrix match for the angular dependence, but the energy dependence doesn't.