Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves

TL;DR

This paper demonstrates that field theories on plane wave backgrounds possess a well-defined S-matrix formulation for 2-to-2 scattering processes, supported by detailed analysis of four-point functions.

Contribution

It provides the first detailed analysis showing the existence of an S-matrix for scalar and gauge field theories on plane wave backgrounds.

Findings

Four-point functions are well-behaved and interpretable as S-matrix elements.

Field theories on plane wave backgrounds support a classical S-matrix formulation.

Abstract

Field theories on the plane wave background are considered. We discuss that for such field theories one can only form 1+1 dimensional freely propagating wave packets. We analyze tree level four point functions of scalar field theory as well as scalars coupled to gauge fields in detail and show that these four point functions are well-behaved so that they can be interpreted as S-matrix elements for 2 particle $\to$ 2 particle scattering amplitudes. Therefore, at least classically, field theories on the plane wave background have S-matrix formulation.