Non-abelian tri-vector deformations in
Ilya Bakhmatov (Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, Lomonosovsky avenue, Moscow, 119991, Russia, Yerevan Physics Institute, Alikhanian Brothers 2, Yerevan, 0036, Armenia)
; Kirill Gubarev (Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, 141700, Russia); 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)
A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form × with the 4-form flux on is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS × $$\mathbbm{S}$$ solution of = 11 supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS × $$\mathbbm{S}$$ .