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 ${\text{M}}_7\times {\text{S}}^3$, 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.

26 pages + appendices. Version 2: fixed typos and added references. Version 3: published version, more typos fixed

References in corpus (15)

• Generalised Geometry for M-Theory
• On non-abelian T-dual geometries with Ramond fluxes
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• Yang-Baxter sigma models based on the CYBE
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• Polyvector deformations in eleven-dimensional supergravity
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Non-abelian U-duality at work
• Non-abelian T-folds
• Thermodynamics of $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed conformal field theories
• An Algebraic Classification of Solution Generating Techniques

Cited by in corpus (1)

• Generalised U-dual solutions via ISO(7) gauged supergravity