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

Particle production in integrable field theories may exist depending on the vacuum around which excita-tions are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable A.-deformed model for SU (2) together with a timelike coordinate. We construct the corre-sponding four-dimensional plane wave background (a deformation of the Nappi-Witten solution) keeping also post-plane wave corrections, as well as all the non-trivial A.-dependence. After imposing the classical light-cone gauge and the Virasoro constraints, we obtain an interacting field theory for the transverse physi-cal 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 A.-deformation parameter. In addition, we compute the S-matrix for the two-particle elastic scattering exactly in A. and to leading order in the large k-expansion. Our method can be applied to any integrable theory with at least one isometry in order to check the classical integrability of the parent theory.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

This article investigates the particle production and scattering problems in the integrable A.-deformed model for SU(2). A four-dimensional plane wave background is constructed, and the absence of particle production to leading order in the large k-expansion is demonstrated. The S-matrix for two-particle elastic scattering is also calculated.