# 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.

## Key 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.