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 Θ of the non-commutative structure Θ used for non-Abelian T-duality or integrable deformations does not give correct mathcal{J} for Poisson-Lie T-plurality.