A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form M 4 × M 7 with the 4-form flux on M 4 is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS 4 × S 7 solution of d = 11 supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS 4 × S 7 .

No abstract

We develop a procedure to reproduce the ten-dimensional generalized supergravity equations from T-duality covariant equations, that facilitates generalization to Uduality covariant formulations of eleven-dimensional supergravity. The latter leads to a modification of the eleven-dimensional supergravity equations with terms that contain a rank-2 tensor field J mn which is the eleven-dimensional analog of the non-unimodularity Killing vector I m in ten dimensions.

In arXiv:2203.03372 [Phys.Rev.D 105 (2022) 8, L081904] we presented a modification of 11-dimensional supergravity field equations which upon dimensional reduction yields generalized supergravity equations in 10-dimensions. In this paper we provide full technical details of that result which is based on SL(5) exceptional field theory. The equations are obtained by making a non-unimodular tri-vector Yang-Baxter deformation which breaks the initial GL(11) symmetry down to GL(7)×GL(4). We also give some non-trivial solutions to these equations.

This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for integrability of two-dimensional systems. Particular focus is given to Nambu structures and loop variables naturally appearing in membrane dynamics. While reviewing each topic in more details we emphasize connections between them and speculate on possible relations to membrane integrability.