Integrable deformations of the flat space sigma model

TL;DR

This paper introduces a new integrable deformation of the flat space sigma model that preserves a Lax connection, enabling the study of novel backgrounds with constant or linear H-flux and analyzing their symmetries.

Contribution

It defines a specific deformation operator for the flat space sigma model that maintains integrability and explores resulting backgrounds and symmetries.

Findings

Found flat space with arbitrary constant H-flux

Discovered Nappi-Witten and related backgrounds with constant H-flux

Identified symmetry structures including deformed translation symmetries

Abstract

We explore a deformation of the flat space symmetric space sigma model action. The deformed action is designed to allow a Lax connection for the equations of motion, similar to the undeformed model. For this to work, we identify a set of constraints that the deformation operator, which is incorporated into the action, must fulfil. After defining the deformation, we explore simple solutions to these constraints and describe the resulting deformed backgrounds. Specifically, we find flat space in Cartesian coordinates with arbitrary constant $H$-flux or linear $H$-flux in a light cone coordinate. Additionally, we find the Nappi-Witten background along with various Nappi-Witten-like backgrounds with near arbitrary constant $H$-flux. Finally, we discuss the symmetries of the deformed models, finding that the deformed symmetries will always include a set of symmetries that in the undeformed limit becomes the total set of translations.