Poisson–Lie T-plurality with spectators

In this paper we investigate Poisson–Lie transformation of dilaton and vector field $${\mathcal {J}}$$ J appearing in generalized supergravity equations. While the formulas appearing in literature work well for isometric sigma models, we present examples for which generalized supergravity equations are not preserved. Therefore, we suggest modification of these formulas.

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“…Here we shall recapitulate well known basics of Poisson-Lie T-plurality with spectators [1,2,10] to establish notation.…”

Section: Basics Of Poisson-lie T-pluralitymentioning

confidence: 99%

Poisson–Lie transformations and generalized supergravity equations

Hlavatý

Petr

2021

Eur. Phys. J. C

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“…In this Section we will summarize main features of Poisson-Lie T-duality and plurality [15][16][17]43], Generalized Supergravity Equations [9][10][11] and T-folds [19,21,[27][28][29]44]. For detailed information see the original papers.…”

Section: Preliminariesmentioning

confidence: 99%

T-folds as Poisson–Lie plurals

Hlavatý

Petr

2020

Eur. Phys. J. C

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In previous papers we have presented many purely bosonic solutions of Generalized Supergravity Equations obtained by Poisson–Lie T-duality and plurality of flat and Bianchi cosmologies. In this paper we focus on their compactifications and identify solutions that can be interpreted as T-folds. To recognize T-folds we adopt the language of Double Field Theory and discuss how Poisson–Lie T-duality/plurality fits into this framework. As a special case we confirm that all non-Abelian T-duals can be compactified as T-folds.

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“…Components of the dual tensor F obtained by the non-Abelian T-duality transformation are [3] F that further restrict the functions ξ µ . Formula (33) for the non-Abelian T-duality of σ-models with spectators follow from the Poisson-Lie T-duality formulated in the framework of the Drinfel'd double [3,4,6]. By this formula we get dual tensors whose components will depend on functions ξ µ or X ξ mapping for fixed s from the group G to the invariant manifold Σ(s).…”

Section: Dualizationmentioning

confidence: 99%

On uniqueness of T-duality with spectators

Hlavatý

Petrasek

2016

Int. J. Mod. Phys. A

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We investigate the dependence of nonabelian T-duality on various identification of the group of target space isometries of nonlinear sigma models with its orbits, i.e. with respect to the location of the group unit on manifolds invariant under the isometry group. We show that T-duals constructed by isometry groups of dimension less than the dimension of the (pseudo)riemannian manifold may depend not only on the initial metric but also on the choice of manifolds defining positions of group units on each of the submanifold invariant under the isometry group. We investigate whether this dependence can be compensated by coordinate transformation.Comment: 11 pages, an introductory example added, some typos correcte

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Poisson–Lie T-plurality with spectators

Cited by 10 publications

References 12 publications

Poisson–Lie transformations and generalized supergravity equations

Poisson–Lie transformations and generalized supergravity equations

T-folds as Poisson–Lie plurals

On uniqueness of T-duality with spectators

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