Polyvector deformations in eleven-dimensional supergravity

TL;DR

This paper explores specific deformations of 11-dimensional supergravity backgrounds using exceptional field theory, deriving conditions for these deformations to produce valid solutions and connecting them to algebraic structures like the Yang-Baxter equation.

Contribution

It introduces new conditions for 3- and 6-vector deformations in supergravity backgrounds and links these to exceptional algebraic structures, extending classical integrability concepts.

Findings

Derived sufficient conditions for deformations to be solutions.

Connected deformations to exceptional Drinfeld algebra.

Identified additional constraints possibly related to higher algebraic structures.

Abstract

We consider 3- and 6-vector deformations of 11-dimensional supergravity backgrounds of the form $M_5\times M_6$ admitting at least 3 Killing vectors. Using flux formulation of the E${}_{6(6)}$ exceptional field theory we derive (sufficient) conditions for the deformations to generate a solution. In the group manifold case these generalisations of the classical Yang-Baxter equation for the case of r-matrices with 3 and 6 indices are shown to reproduce those obtained from exceptional Drinfeld algebra for E${}_{6(6)}$. In general we see an additional constraint, which might be related to higher exceptional Drinfeld algebras.