Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids

Blumenhagen, Ralph; Deser, Andreas; Plauschinn, Erik; Rennecke, Felix

doi:10.1007/jhep02(2013)122

Cited by 63 publications

(75 citation statements)

References 36 publications

(96 reference statements)

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“…Using the torus derivatives: 19) together with the classical part of X, given in eq. (4.14), and that of Y: 20) one obtains the non-trivial contribution to the partition function:…”

Section: T-duality In the Basementioning

confidence: 99%

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Condeescu

Florakis

Kounnas

et al. 2013

J. High Energ. Phys.

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Abstract:We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes. Exploiting the connection between internal fluxes and structure constants of the gaugings in the reduced supergravity theory, we can identify the types of fluxes arising in certain classes of freely-acting symmetric and asymmetric orbifolds. We give a general procedure for deriving the gauge algebra of the effective gauged supergravity using the exact CFT description at the orbifold point. We find that the asymmetry is, in general, related to the presence of non-geometric Q-and R-fluxes. The action of T-duality is studied explicitly on various orbifold models and the resulting transformation of the fluxes is derived. Several explicit examples are provided, including compactifications with geometric fluxes, Q-backgrounds (T-folds) and R-backgrounds. In particular, we present an asymmetric Z 4 × Z 2 orbifold in which all geometric and nongeometric fluxes ω, H, Q, R are turned on simultaneously. We also derive the corresponding flux backgrounds, which are not in general T-dual to geometric ones, and may even simultaneously depend non-trivially on both the coordinates and their winding T-duals.

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“…Using the torus derivatives: 19) together with the classical part of X, given in eq. (4.14), and that of Y: 20) one obtains the non-trivial contribution to the partition function:…”

Section: T-duality In the Basementioning

confidence: 99%

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Condeescu

Florakis

Kounnas

et al. 2013

J. High Energ. Phys.

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show abstract

“…In particular, eq. (4.23) of [9] is formally the same as ours (2.17), if we identify their β as our θ.…”

Section: Future Directionsmentioning

confidence: 77%

“…The approach [9] is conceptually similar to the content of §2 of this paper. The authors consider a quasi-Poisson version of our Lie algebroid (T * M ) θ and regard their R-flux as the violation of the Poisson condition due to the quasi-Poisson structure.…”

Section: Future Directionsmentioning

confidence: 99%

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Gravity theory on Poisson manifold with R‐flux

Asakawa

Muraki

Watamura

2015

Fortschritte der Physik

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A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi-Civita connection, which is based on the Lie algebroid of a Poisson manifold. Then, we show that in Poisson Generalized Geometry the R-fluxes are consistently coupled with such a gravity. An R-flux appears as a torsion of the corresponding connection in a similar way as an H-flux which appears as a torsion of the connection formulated in the standard Generalized Geometry. We give an analogue of the Einstein-Hilbert action coupled with an R-flux, and show that it is invariant under both β-diffeomorphisms and β-gauge transformations.

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“…Upon implementing the projection∂ i = 0, one recovers the usual action of supergravity. In particular, by performing a formal T-duality transformation and a field redefinition in the double field theory action using the O(d, d) transforms of the generalized geometry formalism, one can in this way obtain a field theory on M for the non-geometric fluxes [6] (see also [12]). An alternative target space perspective is described in [4] at purely the supergravity level.…”

Section: Pos(icmp 2013)007mentioning

confidence: 99%

Nonassociative geometry and twist deformations in non-geometric string theory

Mylonas¹,

Schupp²,

Szabo

2014

Proceedings of Third International Satellite Conference on Mathematical Methods in Physics — PoS(ICMP 2013)

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We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries propagate in the phase space of the target space compactification, equiped with a twisted Poisson structure. The effective membrane target space is determined by the standard Courant algebroid over the target space twisted by an abelian gerbe in momentum space. Quantization of the membrane sigma-model leads to a proper quantization of the non-geometric background, which we relate to Kontsevich's formalism of global deformation quantization that constructs a noncommutative nonassociative star product on phase space. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras canonically associated to the twisted Courant algebroid, and cochain twist quantization using suitable quasi-Hopf algebras of symmetries in the phase space description of R-space which constructs a Drinfel'd twist with non-trivial 3-cocycle. We illustrate and apply our formalism to present a consistent phase space formulation of nonassociative quantum mechanics.

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Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids

Cited by 63 publications

References 36 publications

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Gravity theory on Poisson manifold with R‐flux

Nonassociative geometry and twist deformations in non-geometric string theory

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