Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Abstract

Poisson-Lie T-duality and plurality are important solution generating techniques in string theory and (generalized) supergravity. Since duality/plurality does not preserve conformal invariance, the usual beta function equations are replaced by Generalized Supergravity Equations containing vector $\mathcal{J}$. In this paper we apply Poisson-Lie T-plurality on Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and $\mathcal{J}$ satisfy the Generalized Supergravity Equations. The procedure is valid also for non-local dilaton and non-constant $\mathcal{J}$. We also show that $Div\Theta$ of the non-commutative structure $\Theta$ used for non-Abelian T-duality or integrable deformations does not give correct $\mathcal{J}$ for Poisson-Lie T-plurality.

v3 - published version

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• Non-abelian U-duality at work
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• More on Doubled Aspects of Algebroids in Double Field Theory
• Poisson-Lie transformations and Generalized Supergravity Equations
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations
• T-folds as Poisson-Lie plurals
• Classification of standard Manin triples in dimension 4+4
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• Plane-parallel waves as Jacobi-Lie models
• On spectator dependence of Jacobi-Lie T-plurality