Yang-Baxter deformations of the flat space string

TL;DR

This paper develops a framework for Yang-Baxter deformations of flat space string models, preserving integrability, and explores both homogeneous and inhomogeneous cases with explicit examples in Minkowski space.

Contribution

It introduces a method to perform Yang-Baxter deformations on non-semi-simple symmetric space sigma models, including flat space strings, extending previous approaches.

Findings

Homogeneous deformations preserve Lax connection form similar to semi-simple cases.

Inhomogeneous deformations require modified algebraic structures.

Explicit nonabelian deformation examples in 3D Minkowski space.

Abstract

We define integrability preserving Yang-Baxter deformations of symmetric space sigma models with non-semi-simple symmetry group, in particular the flat space string, using only the essential structures of a symmetric space sigma model. For homogeneous deformations, the Lax connection is of the same form as the semi-simple case, although the R operator no longer satisfies a freestanding operator equation. For inhomogeneous deformations, the form of the Lax connection needs to be relaxed, by modifying the underlying algebra. We illustrate the construction by discussing nonabelian deformations of three dimensional Minkowski space.