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

• Received 8 December 2020
• Accepted 3 March 2021

DOI:https://doi.org/10.1103/PhysRevD.103.066021

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Published by the American Physical Society