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.
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Hlavatý, L., Petr, I. Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations. J. High Energ. Phys. 2020, 68 (2020). https://doi.org/10.1007/JHEP04(2020)068
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DOI: https://doi.org/10.1007/JHEP04(2020)068