Non-isometric U-dualities

TL;DR

This paper explores generalized U-duality transformations that do not depend on isometries, extending the framework to include non-isometric directions and relating them to algebraic structures and deformations in supergravity.

Contribution

It introduces a new class of U-duality transformations applicable without isometries and connects them to six-vector deformations involving E6(6) actions in supergravity.

Findings

Generalized U-duality maps between type IIA and 11D supergravity solutions.

Identification of six-vector deformations involving E6(6) acting on non-isometric directions.

Comparison of these deformations with Yang-Baxter deformations.

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 $\text{M}_7 \times \text{S}^3$, 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 $\text{M}_7$ 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 $\mathrm{E}_{6(6)}$ 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.