Polyvector deformations in eleven-dimensional supergravity

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.

20 pages + Appendix

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• Generalizing eleven-dimensional supergravity
• Generalized 11D supergravity equations from tri-vector deformations
• Jacobi-Lie T-plurality
• Tri-vector deformations on compact isometries
• Integrability structures in string theory
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• Non-isometric U-dualities
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• Yang-Baxter structure of the extended space
• Generalised U-dual solutions in supergravity
• Brane bound states, deformations and OM