Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production

TL;DR

This paper investigates particle scattering in integrable pp-wave backgrounds, demonstrating the absence of particle production and providing exact S-matrix calculations for a deformed SU(2) model, highlighting the role of integrability and deformation parameters.

Contribution

The study constructs a four-dimensional integrable pp-wave background with a $ ext{SU}(2)$ $ ext{lambda}$-deformation, explicitly shows no particle production at leading order, and computes the exact two-particle S-matrix in $ ext{lambda}$.

Findings

No particle production at leading order in large $k$-expansion.

Exact two-particle S-matrix computed in $ ext{lambda}$-deformed model.

Interaction vertices depend crucially on the $ ext{lambda}$-deformation parameter.

Abstract

Particle production in integrable field theories may exist depending on the vacuum around which excitations are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable $\lambda$-deformed model for $SU(2)$ together with a timelike coordinate. We construct the corresponding four-dimensional plane wave background keeping also post-plane wave corrections, as well as all the non-trivial $\lambda$-dependence. After imposing the light-cone gauge and the Virasoro constraints, we obtain an interacting field theory for the transverse physical modes which are massive. We explicitly demonstrate the absence of particle production to leading order in the large $k$-expansion. This is based crucially on the form of the interaction vertices and their dependence on the $\lambda$-deformation parameter. In addition, we compute the $S$-matrix for the two-particle elastic scattering exactly in $\lambda$ and to leading order in the large $k$-expansion. Our method can be applied to any integrable theory with at least one isometry.