Duality twisted reductions of Double Field Theory of Type II strings

Özer, Aybike Çatal

doi:10.1007/jhep09(2017)044

Cited by 11 publications

(53 citation statements)

References 67 publications

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“…where C is the charge conjugation matrix. For more details, see [38] and [53]. The factors S θ and S β in S NATD are the Spin + (10, 10) elements that projects onto the SO + (10, 10) matrix that generates the B-transformations and β-shifts with θ IJ = ν K C K IJ and β IJ = ν K C K IJ , respectively.…”

Section: Natd As An O(d D) Transformationmentioning

confidence: 99%

“…As the O(10, 10) matrix that produces the NATD fields is not constant, it is not immediately clear that it generates a solution generating transformation for DFT. To show that this is indeed the case, we find it useful to utilize the framework of Gauged Double Field Theory (GDFT), which is obtained by a duality twisted (Scherk-Schwarz) reduction [49] of DFT [50]- [53]. GDFT is a deformation of DFT, determined by the fluxes associated with the twist matrix that define the duality twisted reduction anzats.…”

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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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Section: Natd As An O(d D) Transformationmentioning

confidence: 99%

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confidence: 99%

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

Çatal-Özer

2019

J. High Energ. Phys.

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“…Here, ψ α , α = (I, a) are the Clifford algebra elements ψ α = 1/ √ 2Γ α , where Γ α are the Gamma matrices. For more details, see [68]. For index conventions, see Appendix (C).…”

Section: Transformation Of the Rr Fieldsmentioning

confidence: 99%

“…The gauge algebra of infinitesimal transformations under generalized diffeomorphisms closes under the C-bracket. For more details see [68], [69].…”

Section: A Brief Review Of Dftmentioning

confidence: 99%

“…Since generalized supergravity equations can be embedded in DFT [55], [56], [57], one concludes that the DFT fields constructed out of the YB deformed target space field constitute a solution for the field equations of DFT. Using the results from [25], this allows us to extract DFT fields which form a solution of gauged double field theory (GDFT) [58], [59], [60], [61] determined by the fluxes associated with the YB matrix. This then gives us a handle on exploring the gravity/CYBE correspondence proposed in [14], [15], [16] and perhaps extending it to a DFT/CYBE correspondence.…”

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Yang–Baxter deformation as an $\boldsymbol {O(d,d)}$ transformation

Çatal-Özer

Tunalı

2020

Class. Quantum Grav.

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We show that the homogeneous Yang-Baxter (YB) deformation of Green-Schwarz sigma models manifests itself as the action of a coordinate dependent O(d, d) matrix on the target space fields both in the NS-NS and the RR sectors. When the R-matrix that determines the YB deformation is Abelian, the O(d, d) matrix reduces to the constant matrix that produces Lunin-Maldacena deformations (TsT deformations), in agreement with the well established fact that homogeneous YB deformations are a generalization of LM deformations. Our approach gives a natural embedding of the homogeneous YB model in Double Field Theory (DFT), a framework which provides an O(d, d) covariant formulation for effective string actions. We show that the YB deformed fields can be regarded as duality twisted fields in the context of Gauged Double Field Theory (GDFT). We compute the fluxes associated with the twist and show that the conditions on the R-matrix determining the YB deformation give rise to conditions on the fluxes on the (G)DFT side. We find that the R-flux vanishes if and only if the R-matrix satisfies the classical Yang-Baxter equation, and the unimodularity of the R-matrix implies that the Q-flux is traceless. Non-unimodularity of the R-matrix forces the generalized dilaton field to pick up a linear dependence on the winding type coordinates of DFT, implying that the corresponding supergravity fields should satisfy generalized supergravity equations. ♯ ozerayb@itu.edu.tr ♭ tunali16@itu.edu.tr IntroductionConstructing integrable deformations of string backgrounds relevant for AdS/CFT correspondence is an active line of research. An important milestone in this direction was the work of Klimcik [1], where he introduced a particular type of deformation for Principal Chiral Models (PCM) with simple compact Lie group as the target manifold. The resulting deformed sigma model was dubbed Yang-Baxter sigma model, as the deformation is based on solutions of modified classical Yang-Baxter equation (mCYBE). The integrability of the YB sigma model was proved later in [2]. The applicability of YB deformations was extended to symmetric coset spaces in [3], which in turn was applied to AdS 5 × S 5 in [4]. The NS-NS sector of the corresponding deformed supergravity background was found in [5]. Similar deformations for the NS-NS sector of AdS n × S n supercosets was studied in [6]. The RR sectors of these deformed backgrounds was worked out in [7], and was successfully established for the n = 2 and n = 3 cases. The most interesting n = 5 case could not be understood fully in that work and the full Lagrangian for the deformed AdS 5 × S 5 was found later in [8]. We should note that such deformations of the supergravity backgrounds are usually called η-deformations.It is also possible to consider similar deformations based on the classical Yang-Baxter equation (CYBE), as opposed to mCYBE. Following the literature, we call the resulting models homogeneous Yang-Baxter models. Such deformations of the AdS 5 × S 5 string was first studied in [9]. These deformatio...

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L∞ algebras and tensor hierarchies in Exceptional Field Theory and Gauged Supergravity

Cagnacci

Codina

Marqués

2019

J. High Energ. Phys.

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We show how the gauge and field structure of the tensor hierarchies in Double and E 7(7)Exceptional Field Theory fits into L ∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gaugingdependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.

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Duality twisted reductions of Double Field Theory of Type II strings

Cited by 11 publications

References 67 publications

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

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

Yang–Baxter deformation as an $\boldsymbol {O(d,d)}$ transformation

L∞ algebras and tensor hierarchies in Exceptional Field Theory and Gauged Supergravity

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