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

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

doi:10.1088/1361-6382/aaaeed

Cited by 3 publications

(9 citation statements)

References 40 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 Ofsupporting

confidence: 51%

“…This background was found in [37] as non-Abelian T-dual of flat metric. Dilaton that together with (42) satisfies beta function equations iŝ…”

Section: Transformation Ofmentioning

confidence: 98%

“…Mappings C that transform the algebraic structure of Manin triple b V I −1 ⊲⊳ a to b V ⊲⊳ a are given by matrices inverse to (37) and (38). After a suitable change of coordinates we find that backgrounds obtained from these general solutions differ from background…”

Section: Formula (20) For New Dilatonsmentioning

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: Transformation Ofsupporting

confidence: 51%

“…This background was found in [37] as non-Abelian T-dual of flat metric. Dilaton that together with (42) satisfies beta function equations iŝ…”

Section: Transformation Ofmentioning

confidence: 98%

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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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“…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%

“…One may also ask why Buscher duality with respect to V 2 is not included in (23) or (24). The reason is that change of bases…”

Section: Poisson-lie T-dualitymentioning

confidence: 99%

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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A Tour of T-duality: Geometric and Topological Aspects of T-dualities

Bugden¹

2019

Preprint

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The primary focus of this thesis is to investigate the mathematical and physical properties of spaces that are related by T-duality and its generalisations. In string theory, T-duality is a relationship between two a priori different string backgrounds which nevertheless behave identically from a physical point of view. These backgrounds can have different geometries, different fluxes, and even be topologically distinct manifolds. T-duality is a uniquely 'stringy' phenomenon, since it does not occur in a theory of point particles, and together with other dualities has been incredibly useful in elucidating the nature of string theory and M-theory.There exist various generalisations of the usual T-duality, some of which are still putative, and none of which are fully understood. Some of these dualities are inspired by mathematics and some are inspired by physics. These generalisations include non-abelian T-duality, Poisson-Lie T-duality, non-isometric T-duality, and spherical T-duality. In this thesis we review T-duality and its various generalisations, studying the geometric, topological, and physical properties of spaces related by these dualities.

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

Cited by 3 publications

References 40 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?

A Tour of T-duality: Geometric and Topological Aspects of T-dualities

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