Non-Abelian T-duality as a Transformation in Double Field Theory

Abstract

Non-Abelian T-duality (NATD) is a solution generating transformation for supergravity backgrounds with non-Abelian isometries. We show that NATD can be described as a coordinate dependent O(d,d) transformation, where the dependence on the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group. Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions. As a result of this embedding, it becomes easy to prove that the NATD transformed backgrounds solve supergravity equations, when the isometry algebra is unimodular. If the isometry algebra is non-unimodular, the generalized dilaton field is forced to have a linear dependence on the dual coordinates, which implies that the resulting background solves generalized supergravity equations.

arXiv commenttypos and signs corrected; references added

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• The Geometry, Branes and Applications of Exceptional Field Theory
• U-duality extension of Drinfel'd double
• Poisson-Lie U-duality in Exceptional Field Theory
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Quantum correction to generalized T-dualities
• Generalized Dualities and Higher Derivatives
• Exploring Exceptional Drinfeld Geometries
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Non-isometric U-dualities
• Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality
• Generalised U-dual solutions in supergravity