Tri-vector deformations on compact isometries

TL;DR

This paper explores tri-vector deformations in supergravity, demonstrating that unlike bi-vector deformations constrained by the classical Yang-Baxter equation, tri-vector deformations governed by a generalized equation can preserve isometries in certain backgrounds.

Contribution

It provides explicit examples of tri-vector deformations in 11d supergravity, contrasting with the limitations of bi-vector deformations governed by the classical Yang-Baxter equation.

Findings

Tri-vector deformations preserve isometries of AdS7xS4.

Explicit examples of deformations in 11d supergravity backgrounds.

Contrast between bi-vector and tri-vector deformation constraints.

Abstract

Classical Yang-Baxter equation governing bi-vector deformations of 10d supergravity is known to have no solutions along non-abelian compact isometries. By providing explicit examples we show that this is in contrast to generalized Yang-Baxter equation governing tri-vector deformations of 11d supergravity. We present deformations of the AdS7xS4 and flat backgrounds with isometries generated by Killing vectors of a sphere. Isometries of the AdS space-time are preserved by such deformations.