Non-abelian T-folds

Bugden, Mark

doi:10.1007/jhep03(2019)189

Cited by 21 publications

(19 citation statements)

References 44 publications

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“…This is a non-geometric U-duality transformation, and we can then further view the fluxf abc d as an M-theory non-geometrc Q-flux [39]. This is the generalisation of the interpretation of non-Abelian T-dual geometries as T-folds [40].…”

Section: Three-algebra Geometriesmentioning

confidence: 92%

Exploring exceptional Drinfeld geometries

Blair

Thompson

Zhidkova

2020

J. High Energ. Phys.

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We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. We provide examples including “three-algebra geometries”, which encode the structure constants for three-algebras and in some cases give novel uplifts for CSO(p, q, r) gaugings of seven-dimensional maximal supergravity. We also discuss the M-theoretic embedding of both non-Abelian and Poisson-Lie T-duality.

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Section: Three-algebra Geometriesmentioning

confidence: 92%

Exploring exceptional Drinfeld geometries

Blair

Thompson

Zhidkova

2020

J. High Energ. Phys.

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“…Very recently, a paper has appeared which also views NATD as an O(d, d) transformation [25]. See also [26], which has a similar approach to NATD.Besides making calculations significantly easier, our approach makes it possible to view 1 The fact that the NATD background fails to satisfy standard supergravity equations when G is nonunimodular was first noted in [20] and the generalized equations appeared first in [21]. For a detailed account, see [22].…”

mentioning

confidence: 95%

“…Very recently, a paper has appeared which also views NATD as an O(d, d) transformation [25]. See also [26], which has a similar approach to NATD.…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian T-duality as a transformation in Double Field Theory

Çatal-Özer

2019

J. High Energ. Phys.

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Non-Abelian T-duality (NATD) is a solution generating transformation for supergravity backgrounds with non-Abelian isometries. We show that NATD can be described as a coordinate dependent O(d,d) transformation, where the dependence on the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group. Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions. As a result of this embedding, it becomes easy to prove that the NATD transformed backgrounds solve supergravity equations, when the isometry algebra is unimodular. If the isometry algebra is nonunimodular, the generalized dilaton field is forced to have a linear dependence on the dual coordinates, which implies that the resulting background solves generalized supergravity equations. IntroductionNon-Abelian T-duality (NATD) is a generalization of T-duality for strings on backgrounds with non-Abelian isometries [1]- [5]. Although it is not as well established as T-duality is as a string duality symmetry, it works well as a solution generating transformation for supergravity. The rules for the transformation of the fields in the NS-NS sector, namely the metric, the B-field and the dilaton field has been known for a long time. Recently, NATD has gained a new interest, as the rules for the transformation of the fields in the RR sector of Type II strings has also been found [6]. This has been applied to many supergravity backgrounds by various groups, especially to backgrounds that are relevant for AdS-CFT correspondence, see for example [7]-[16].Recently, a compact formula for the transformation of the supergravity fields for a generic Green-Schwarz string with isometry G has been obtained in [17], where they also showed that the sigma model after NATD has kappa symmetry. This means that the resulting background is a solution of the generalized supergravity equations (GSE), which have recently been introduced in [18] as a generalization of supergravity equations, see also [19]. To be more precise, when the isometry group G is unimodular, the dualized sigma model is Weyl invariant and the target space is a solution of standard Type II supergravity equations. If G is non-unimodular so that the structure constants of the Lie algebra of G is not traceless, the trace components give rise to a deformation of the equations to be satisfied by the target space fields to GSE 1 .The purpose of this paper is to describe the NATD transformation rules obtained in [17] as a coordinate dependent O(10, 10) transformation 2 . In Abelian T-duality with d commuting isometries, the transformation rules for the supergravity fields in the NS-NS sector can be neatly described through the action of a constant O(d, d) matrix embedded in O(10, 10) [23]. The RR fields are then packaged in a differential form, which can be a regarded as a spinor field that transforms under Spin(d, d). If the...

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“…on a semi-Abelian Drinfel'd double D = (G |A ), can be compactified as Tfolds in coordinatesx. In a different way this has been shown also in [42].…”

Section: Short Review Of Double Field Theory and T-foldsmentioning

confidence: 59%

“…From the structure of Drinfel'd double underlying non-Abelian T-duality one finds that all non-Abelian T-duals can be compactified as T-folds (as noticed e.g. in [42]). In the case of general plurality transformation additional conditions have to be satisfied.…”

Section: Introductionmentioning

confidence: 88%

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 T-folds

Cited by 21 publications

References 44 publications

Exploring exceptional Drinfeld geometries

Exploring exceptional Drinfeld geometries

Non-Abelian T-duality as a transformation in Double Field Theory

T-folds as Poisson–Lie plurals

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