Poisson–Lie identities and dualities of Bianchi cosmologies

Hlavatý, Ladislav; Petr, I.

doi:10.1140/epjc/s10052-019-7356-5

Cited by 3 publications

(9 citation statements)

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“…There is rather large number of solutions of equations (9) and (10) giving linear mappings (6) between generators of b III ⊲⊳ a and b III ⊲⊳ b II (cf. the table of Poisson-Lie identities of b III ⊲⊳ a in [16]). However, up to a change of coordinates and gauge shift of the B field, all the resulting plural backgrounds F on G are equivalent.…”

Section: Bianchi III Cosmologymentioning

confidence: 99%

“…This example shows that components of left-invariant fields need to appear in formulas (23), (24). Papers [14], [16] dealt only with semi-Abelian Drinfel'd doubles whereV a,m = δ a,m , vectorsJ were constant and proportional to the trace of structure constants so the full form of (24) was not necessary.…”

Section: Bianchi III Cosmologymentioning

confidence: 99%

“…Authors of [14] have found non-Abelian T-duals of Bianchi cosmologies [15] and have shown that dual backgrounds indeed satisfy Generalised Supergravity Equations. In our recent paper [16] we noted that beside "full" non-Abelian T-dualities used in [14] there are other transformations that belong to the NATD-group investigated in [17]. Namely, we considered Bshifts, β-shifts, "factorized" dualities and their compositions and we have shown that backgrounds obtained by these transformations satisfy Generalized Supergravity Equations as well.…”

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confidence: 99%

“…Decompositions of such Drinfel'd doubles were classified in [22] in terms of Manin triples. It turns out that for each group B there are several Manin triples and many embedings of these Manin triples into d. Resulting plural backgrounds depend on many constants [16] and it is a tremendous task to put down complete classification. Since it is not always possible to present full results, we often restrict to particular examples of Poisson-Lie T-plurality to show important features of obtained models.…”

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confidence: 99%

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Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Hlavatý

Petr

2020

J. High Energ. Phys.

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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 J . In this paper we apply Poisson-Lie Tplurality on Bianchi cosmologies. We present a formula for the vector J as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and J satisfy the Generalized Supergravity Equations. The procedure is valid also for non-local dilaton and non-constant J . We also show that Div Θ of the noncommutative structure Θ used for non-Abelian T-duality or integrable deformations does not give correct J for Poisson-Lie T-plurality. * hlavaty@fjfi.cvut.cz † ivo.petr@fit.cvut.cz ContentsG andḠ that may depend on coordinates of the dual group leading to puzzle discussed in [23]. Inspired by [21] we show how to deal with this issue and present formulas that allow us to calculate vector field J appearing in Generalized Supergravity Equations. The plural backgrounds, dilatons and J then satisfy these equations.Authors of [24,25,26] consider Yang-Baxter deformations of AdS 5 × S 5 and calculate vector field J as DivΘ from non-commutative structure Θ in the open string picture. This works for "full" non-Abelian dualities, but not for "factorized" dualities (e.g. some backgrounds obtained in [16]) or more general pluralities.Plan of the paper is following. In next Section we summarize basics of Poisson-Lie T-plurality including transformation of dilaton and write down formulas for vector field J . In Sections 3.1, 3.2 we derive metrics, B-fields and dilatons obtained by Poisson-Lie T-plurality of the flat background, and in Sections 4.2, 4.1 we present metrics, B-fields and dilatons obtained by Poisson-Lie T-plurality of curved Bianchi cosmologies with nontrivial dilaton. It turns out that for appropriately defined vector field J all of them satisfy Generalized Supergravity Equations.

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Section: Bianchi III Cosmologymentioning

confidence: 99%

Section: Bianchi III Cosmologymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Hlavatý

Petr

2020

J. High Energ. Phys.

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“…In [37,38] we have presented many purely bosonic solutions of Generalized Supergravity Equations that were obtained by Poisson-Lie T-duality or plurality transformation of flat and Bianchi cosmologies [39,40]. The purpose of this paper is to present solutions that can be interpreted as T-folds.…”

Section: Introductionmentioning

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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Non-Abelian U -duality for membranes

Sakatani

Uehara

2020

Progress of Theoretical and Experimental Physics

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Abstract The $T$-duality of string theory can be extended to the Poisson–Lie $T$-duality when the target space has a generalized isometry group given by a Drinfel’d double. In M-theory, $T$-duality is understood as a subgroup of $U$-duality, but the non-Abelian extension of $U$-duality is still a mystery. In this paper we study membrane theory on a curved background with a generalized isometry group given by the $\mathcal E_n$ algebra. This provides a natural setup to study non-Abelian $U$-duality because the $\mathcal E_n$ algebra has been proposed as a $U$-duality extension of the Drinfel’d double. We show that the standard treatment of Abelian $U$-duality can be extended to the non-Abelian setup. However, a famous issue in Abelian $U$-duality still exists in the non-Abelian extension.

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Poisson–Lie identities and dualities of Bianchi cosmologies

Cited by 3 publications

References 60 publications

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

T-folds as Poisson–Lie plurals

Non-Abelian U -duality for membranes

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