Yang-Baxter structure of the extended space

TL;DR

This paper demonstrates that certain Yang-Baxter deformations in Einstein-Maxwell dilaton theory are equivalent to coordinate transformations in a higher-dimensional space, revealing a geometric interpretation of these deformations.

Contribution

It establishes a link between Yang-Baxter deformations and coordinate transformations in a parent theory, providing a new geometric perspective on solution-generating techniques.

Findings

Yang-Baxter deformations correspond to coordinate transformations

Deformations are related to KK reduction in Einstein-Maxwell dilaton theory

Bi-vector Yang-Baxter deformations are coordinate transformations in doubled space

Abstract

We construct an analogue of Yang--Baxter deformations defined by a single Killing vector, that is a solution generating transformation in Einstein--Maxwell dilaton theory. We show that these are nothing but a coordinate transformation in a parent theory related to EMd theory by KK reduction. Similarly (almost-abelian) bi-vector Yang--Baxter deformations are coordinate transformations in the doubled space.