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

Çatal-Özer, Aybike

doi:10.1007/jhep08(2019)115

Cited by 25 publications

(78 citation statements)

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“…A new formulation of DFT on group manifolds (called DFT WZW ) has been developed in [20][21][22], and in the recent works [23,24], the PL T -duality has been studied in the framework of DFT WZW . In more recent papers [7,25], the non-Abelian T -duality and the PL T -duality have been discussed by using another approach, called the gauged DFT [26][27][28][29][30][31] (see also [32,33] for recent discussion on the Drinfel'd double and related aspects in DFT). Thus, DFT is now not restricted to Abelian T -duality but can be applied also to the non-Abelian extensions.…”

Section: Introductionmentioning

confidence: 99%

U -duality extension of Drinfel’d double

Sakatani

2020

Progress of Theoretical and Experimental Physics

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Abstract A family of algebras $\mathcal{E}_n$ that extends the Lie algebra of the Drinfel’d double is proposed. This allows us to systematically construct the generalized frame fields $E_A{}^I$ which realize the proposed algebra by means of the generalized Lie derivative, i.e., $\hat{\pounds}_{E_A}E_B{}^I =-\mathcal{F}_{AB}{}^C\,E_C{}^I$. By construction, the generalized frame fields include a twist by a Nambu–Poisson tensor. A possible application to the non-Abelian extension of $U$-duality and a generalization of the Yang–Baxter deformation are also discussed.

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Section: Introductionmentioning

confidence: 99%

U -duality extension of Drinfel’d double

Sakatani

2020

Progress of Theoretical and Experimental Physics

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“…Recently in [25], we showed that the NATD transformation rules obtained in [24] for a generic GS string with isometry group G can be described through the action of a coordinate dependent 1 See also [23], where they arrive at the same result by utilizing the O(d, d) structure of NATD.…”

Section: Introductionmentioning

confidence: 89%

“…Recently, Borsato and Wulff extended their work to homogeneous YB deformations of more general sigma models than PCMs. In their paper [24], they derived the rules for NATD for a generic Green-Schwarz (GS) string with isometry group G, where NATD is applied with respect to a subgroup of G. Then, by using the connection between NATD and homogeneous YB models that they had established in [21], [22], they proposed the form of homogeneous YB deformation for a generic GS sigma model and showed that this gave a natural generalization of the YB deformation of PCMs and supercosets.Recently in [25], we showed that the NATD transformation rules obtained in [24] for a generic GS string with isometry group G can be described through the action of a coordinate dependent 1 See also [23], where they arrive at the same result by utilizing the O(d, d) structure of NATD.…”

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confidence: 89%

“…Given the relation between NATD and homogeneous YB deformations discussed briefly above, the results of [25] implies that it should be possible to describe YB deformations also as O(d, d) transformations and hence to embed it in DFT. In fact, this approach has already been adopted by several groups.…”

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confidence: 99%

“…The YB matrix we study in this paper is related to the NATD matrix we studied in [25] by a constant O(d, d) transformation. That the two matrices are related is of course not surprising at all, given the fact that [24] constructed the YB deformed models by utilizing the connection with NATD.…”

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confidence: 99%

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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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E6(6) exceptional Drinfel’d algebras

Malek

Sakatani

Thompson

2021

J. High Energ. Phys.

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The exceptional Drinfel’d algebra (EDA) is a Leibniz algebra introduced to provide an algebraic underpinning with which to explore generalised notions of U-duality in M-theory. In essence, it provides an M-theoretic analogue of the way a Drinfel’d double encodes generalised T-dualities of strings. In this note we detail the construction of the EDA in the case where the regular U-duality group is E6(6). We show how the EDA can be realised geometrically as a generalised Leibniz parallelisation of the exceptional generalised tangent bundle for a six-dimensional group manifold G, endowed with a Nambu-Lie structure. When the EDA is of coboundary type, we show how a natural generalisation of the classical Yang-Baxter equation arises. The construction is illustrated with a selection of examples including some which embed Drinfel’d doubles and others that are not of this type.

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

Cited by 25 publications

References 77 publications

U -duality extension of Drinfel’d double

U -duality extension of Drinfel’d double

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

E6(6) exceptional Drinfel’d algebras

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