Tri-vector deformations in $d=11$ supergravity

Abstract

We construct a $d=11$ supergravity analogue of the open-closed string map in the context of SL(5) Exceptional Field Theory (ExFT). The deformation parameter tri-vector $\Omega$ generalizes the non-commutativity bi-vector parameter $\Theta$ of the open string. When applied to solutions in $d=11$, this map provides an economical way of performing TsT deformations, and may be used to recover $d=10$ Yang-Baxter deformations after dimensional reduction. We present a generalization of the Classical Yang-Baxter Equation (CYBE) for rank 3 objects, which emerges from $d=11$ supergravity and the SL(5) ExFT. This equation is shown to reduce to the $d=10$ CYBE upon dimensional reduction.

arXiv comment27 pages; v2: references updated

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• Non-abelian tri-vector deformations in d=11 supergravity
• Exploring Exceptional Drinfeld Geometries
• Polyvector deformations in eleven-dimensional supergravity
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-abelian U-duality at work
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• On non-abelian U-duality of 11D backgrounds
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• Generalizing eleven-dimensional supergravity
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• Tri-vector deformations on compact isometries
• The Stringy Origins of Galileons and their Novel Limit
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• SUSY and tri-vector deformations
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