Eight-dimensional Manin triples, Yang–Baxter deformations and solutions of Supergravity Equations

Abstract

Extensive list of 4+4-dimensional Manin triples that was presented recently can be used to find new solutions of supergravity equations via Poisson–Lie T-plurality. To get the solutions we start with 1+3-dimensional flat backgrounds on Poisson–Lie groups corresponding to semi-Abelian Manin triples. For application of the Poisson–Lie T-plurality we identify Manin triples that form various decompositions of the same Drinfeld double. Beside flat backgrounds and plane-parallel waves solving supergravity equations, plurality transformation also produces curved backgrounds with torsion satisfying (generalized) supergravity equations. Many of the Poisson–Lie transformations can be understood as homogeneous Yang–Baxter deformations. Of special interest are the non-unimodular deformations leading to solutions of generalized supergravity equations.