Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)

TL;DR

This paper demonstrates that Yang-Baxter deformations can be applied beyond coset spaces using an open-closed string map, simplifying the generation of supergravity solutions and extending the applicability of TsT transformations.

Contribution

It proves that the equations of motion in generalized supergravity reduce to the Classical Yang-Baxter Equation for any geometry with isometries, extending Yang-Baxter deformations beyond coset spaces.

Findings

Yang-Baxter deformation equations reduce to CYBE for general geometries.

Provides a systematic method for applying TsT transformations.

Extends the Yang-Baxter solution generating technique to broader settings.

Abstract

Yang-Baxter string sigma-models provide a systematic way to deform coset geometries, such as $AdS_p \times S^p$, while retaining the $\sigma$-model integrability. It has been shown that the Yang-Baxter deformation in target space is simply an open-closed string map that can be defined for any geometry, not just coset spaces. Given a geometry with an isometry group and a bivector that is assumed to be a linear combination of antisymmetric products of Killing vectors, we show the equations of motion of (generalized) supergravity reduce to the Classical Yang-Baxter Equation associated with the isometry group, proving the statement made in [1]. These results bring us closer to the proof of the "YB solution generating technique" for (generalized) supergravity advertised in [1] and in particular provide an economical way to perform TsT transformations.