Symmetries of the 11d supergravity solution space

I will talk about covariant approaches to the study of M-theory vacua, which are called exceptional field theories. I will demonstrate that with their help, polyvector deformations can be determined, making it possible to build entire families using one vacuum solution. The conditions for such deformation are a generalization of the Yang-Baxter equation. In string theory, the appearance of the Yang-Baxter equation is associated with the preservation of integrability of the sigma model on a deformed background; for the case of membranes, the connection with integrability remains an open question. I will also talk about generalized supergravity, which describes the consistent background for the Green-Schwartz string, and how its equations can be obtained using non-unimodular Yang-Baxter deformations. Then I will show a generalization of this method to the 11-dimensional case, with the help of which the equations for generalized 11-dimensional supergravity will be constructed.