Yang-Baxter structure of the extended space

TL;DR

This work investigates Yang–Baxter-type deformations in gravity and supergravity backgrounds by separating them into uni-vector and bi-vector categories. It shows that uni-vector deformations, defined via a single Killing vector, act as coordinate transformations in a higher-dimensional parent theory (via KK reduction) and preserve equations of motion when the Killing condition holds. For bi-vector deformations, the authors demonstrate that certain classes (almost-abelian) act as diffeomorphisms in the doubled space of double field theory, with the classical Yang–Baxter equation arising from the closure of the transformation algebra. Together, these results provide a geometric interpretation of YM–Baxter deformations as coordinate transformations in extended spacetimes, with potential implications for integrability of the associated 2D sigma-models and for generating new solutions in Einstein–Maxwell–dilaton theory. The work also highlights open questions about the unimodularity condition and extensions to tri-vector deformations.

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.