Non-isometric U-dualities

Abstract

I study generalisations of U-duality transformations which do not rely on the existence of isometries. I start by providing more details of a recently proposed generalised U-duality map between solutions of type IIA supergravity of the form M7× S3, with NSNS flux, and solutions of 11-dimensional supergravity, in which the three-sphere is replaced by a four-dimensional geometry which encodes three-algebra structure constants. I then show that when M7 admits two abelian isometries, TsT deformations on the IIA side become six-vector deformations in the 11-dimensional setting. These six-vector deformations involve an action of E6(6) on both isometric and non-isometric directions. I discuss the algebraic interpretation of these deformations, and compare and contrast them with (generalised) Yang-Baxter deformations in supergravity.