Tri-vector deformations in d = 11 supergravity
Ilya Bakhmatov (Kazan Federal University, Institute of Physics, Kremlevskaya 16a, Kazan, 420111, Russia, Asia Pacific Center for Theoretical Physics, Postech, Pohang, 37673, Korea); Nihat Deger (Department of Mathematics, Boğaziçi University, Bebek, Istanbul, 34342, Turkey); Edvard Musaev (Kazan Federal University, Institute of Physics, Kremlevskaya 16a, Kazan, 420111, Russia, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, 141700, Russia); Eoin Colgáin (Asia Pacific Center for Theoretical Physics, Postech, Pohang, 37673, Korea, Department of Physics, Postech, Pohang, 37673, Korea); Mohammad Sheikh-Jabbari (School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran, The Abdus Salam ICTP, Strada Costiera 11, Trieste, 34151, Italy)
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 Ω generalizes the non-commutativity bi-vector parameter Θ 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.