Plane-parallel waves as duals of the flat background II: T-duality with spectators

Petrasek, Filip; Hlavatý, Ladislav; Petr, I.

doi:10.1088/1361-6382/aa7908

Cited by 6 publications

(44 citation statements)

References 39 publications

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“…found earlier in [35,36,37] as non-Abelian T-dual of flat metric. BackgroundsF onḠ found from mappings D 0 · C 1 and D 0 · C 2 can be simplified substantially since after suitable coordinate transformation they differ from background…”

Section: Transformation Ofmentioning

confidence: 50%

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: Transformation Ofmentioning

confidence: 50%

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Hlavatý

Petr

2020

J. High Energ. Phys.

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“…The necessary formulas will be given in the following subsection as a special case of Poisson-Lie T-plurality. In papers [21,22,23], non-Abelian T-duals of sigma model in flat torsionless four-dimensional background were constructed. The groups G were then subgroups of the Poincaré group [24].…”

Section: Poisson-lie T-plurality Of Sigma Modelsmentioning

confidence: 99%

“…Maybe surprisingly, we observe the same phenomenon for Poisson-Lie Tduality as well. Dual sigma models can be obtained by exchange of Manin triples (d, g,g) and (d,g, g) mediated by the matrix (22). On the other hand, there are more general maps between bases of the semi-Abelian Manin triple and its dual.…”

Section: Poisson-lie T-dualitymentioning

confidence: 99%

“…For further investigation we focus on sigma models in four-dimensional target space and introduce spectator fields. In the papers [22], [23] Poisson-Lie T-duality with spectators was used to study non-Abelian T-duals of sigma models in flat Minkowski space. Given the metric η = diag(−1, 1, 1, 1) in coordinates {t, x, y, z}, we consider Killing vectors…”

Section: Sigma Models With Four-dimensional Target Spacementioning

confidence: 99%

“…We have to restrict our calculations to coordinate patches with s 1 = 0. 6 For further details concerning the process of finding the adapted coordinates see [22] where this particular case was denoted S 2,20 .…”

Section: Sigma Models With Four-dimensional Target Spacementioning

confidence: 99%

See 2 more Smart Citations

Poisson-Lie T-plurality revisited. Is T-duality unique?

Hlavatý

Petr

2019

J. High Energ. Phys.

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We investigate (non-)Abelian T-duality from the perspective of Poisson-Lie T-plurality. We show that sigma models related by duality/plurality are given not only by Manin triples obtained from decompositions of Drinfel'd double, but also by their particular embeddings, i.e. maps that relate bases of these decompositions. This allows us to get richer set of dual or plural sigma models than previously thought. That's why we ask how T-duality is defined and what should be the "canonical" duality or plurality transformation.

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Plane-parallel waves as duals of the flat background III: T-duality with torsionless B-field

Hlavatý¹,

Petr²,

Petrasek³

2018

Class. Quantum Grav.

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By addition of non-zero, but torsionless B-field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to one-, two-, three-, and four-dimensional subgroups of Poincaré group. We discuss the influence of the additional B-field on the process of dualization and identify essential parts of the torsionless B-field that cannot be eliminated in general by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics represent plane-parallel waves. Besides the previously found metrics, we find new pp-waves depending on parameters originating from the torsionless B-field. These pp-waves are brought into their standard forms in Brinkmann and Rosen coordinates. *

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Plane-parallel waves as duals of the flat background II: T-duality with spectators

Cited by 6 publications

References 39 publications

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations

Poisson-Lie T-plurality revisited. Is T-duality unique?

Plane-parallel waves as duals of the flat background III: T-duality with torsionless B-field

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