T -folds from Yang-Baxter deformations

Fernandez-Melgarejo, Jose J.; Sakamoto, Jun-ichi; Sakatani, Yuho; Yoshida, Kentaroh

doi:10.1007/jhep12(2017)108

Cited by 48 publications

(79 citation statements)

References 125 publications

(277 reference statements)

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“…This then implies that the R-matrix is unimodular if and only if the Q-flux generated by the YB matrix is traceless, see (4.28). This is in agreement with the results of [39], which also finds that the non-unimodularity of the R-matrix is measured by the trace of the Q-flux. Looking at the expression (4.23), one sees that the trace of the Q-flux is just the divergence of Θ: Q IK I = ∂ I Θ IK , which is the non-commutativity parameter in the language of [42]- [44].…”

Section: The Dilaton Field and The Generalized Supergravity Equationssupporting

confidence: 93%

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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Section: The Dilaton Field and The Generalized Supergravity Equationssupporting

confidence: 93%

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

Çatal-Özer

Tunalı

2020

Class. Quantum Grav.

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“…equations of motion [23,25,28]. However, as pointed out in [145,146], the dual geometry in fact satisfies the generalized supergravity equations of motion (GSE) [147,148]. When the target space satisfies the GSE, string theory has the scale invariance [147,149] and the κ-symmetry [148].…”

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confidence: 99%

Type II DFT solutions from Poisson–Lie $T$-duality/plurality

Sakatani

2019

Progress of Theoretical and Experimental Physics

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String theory has the T -duality symmetry when the target space has Abelian isometries.A generalization of the T -duality, where the isometry group is non-Abelian, is known as the non-Abelian T -duality, which works well as a solution-generating technique in supergravity.In this paper, we describe the non-Abelian T -duality as a kind of O(D, D) transformation when the isometry group acts without isotropy. We then provide a duality transformation rule for the Ramond-Ramond fields by using the technique of double field theory (DFT).We also study a more general class of solution-generating technique, the Poisson-Lie (PL)T -duality or T -plurality. We describe the PL T -plurality as an O(n, n) transformation and clearly show the covariance of the DFT equations of motion by using the gauged DFT.We further discuss the PL T -plurality with spectator fields, and study an application to the AdS 5 × S 5 solution. The dilaton puzzle known in the context of the PL T -plurality is resolved with the help of DFT. IntroductionThe T -duality was discovered in [1] as a symmetry of string theory compactified on a torus.The mass spectrum or the partition function of string theory on a D-dimensional torus was studied for example in [2][3][4][5][6] and the T -duality was identified as an O(D, D; Z) symmetry.It was further studied from a different approach [7,8], and the transformation rules for the background fields (i.e. metric, the Kalb-Ramond B-field, and the dilaton) under the T -duality were determined. In [9,10], the T -duality was understood as an O(D, D) symmetry of the classical equations of motion of string theory. The classical symmetry was clarified in [11] by using the gauged sigma model, and this approach has proved quite useful, for example when we discuss the global structure of the T -dualized background [12]. The transformation rules for the Ramond-Ramond (R-R) fields and spacetime fermions were determined in [13][14][15][16].This well-established symmetry of string theory is called the Abelian T -duality since it relies on the existence of Killing vectors which commute with each other (see [17,18] for reviews).An extension of the T -duality to the case of non-commuting Killing vectors was explored in [19] (see [20,21] for earlier works), and this is known as the non-Abelian T -duality (NATD).Various aspects have been studied in [12,[22][23][24][25][26][27][28][29][30][31][32][33][34][35], but unlike the Abelian T -duality, there are still many things to be clarified. For example, the partition function in the dual model is not the same as that of the original model (see [36] for a recent study), and NATD may rather be regarded as a map between two string theories. The global structure of the dual geometry is also not clearly understood [12]. However, NATD at least generates many new solutions of supergravity, and it can be utilized as a useful solution-generating technique.Under NATD, the isometries are generally broken, and naively we cannot recover the original model from the dual model. However, this issue was re...

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“…To study models generated by I 1 and I 2 we decompose these matrices into product of special elements of NATD group. Namely, we note that I 1 can be written as I 1 = I A · I B where I A is given by (25) and I B is the B-shift (26). Similarly, I 2 can be decomposed as…”

Section: Poisson-lie Identities and Dualitiesmentioning

confidence: 99%

“…Long-lasting problem appearing in discussion of non-Abelian T-duality is that dualization with respect to non-semisimple group G leads to mixed gauge and gravitational anomaly, see [22], proportional to the trace of structure constants of g. Authors of paper [23] have found non-Abelian T-duals of Bianchi cosmologies [24] and have shown that instead of standard β-equations dual backgrounds satisfy the so-called Generalised Supergravity Equations containing Killing vector J whose components are given by the trace of structure constants. For Bianchi V cosmology this was observed already in [25]. Therefore, it is natural to ask if backgrounds and dilatons obtained from Bianchi cosmologies by Poisson-Lie identities and dualities satisfy Generalised Supergravity Equations as well and what Killing vectors have to be used.…”

Section: Introductionmentioning

confidence: 98%

Poisson–Lie identities and dualities of Bianchi cosmologies

Hlavatý

Petr

2019

Eur. Phys. J. C

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We investigate a special class of Poisson-Lie T-plurality transformations of Bianchi cosmologies invariant with respect to non-semisimple Bianchi groups. For six-dimensional semi-Abelian Manin triples b ⊲⊳ a containing Bianchi algebras b we identify general forms of Poisson-Lie identities and dualities. We show that these can be decomposed into simple factors, namely automorphisms of Manin triples, B-shifts, β-shifts, and "full" or "factorized" dualities. Further, we study effects of these transformations and utilize the decompositions to obtain new backgrounds which, supported by corresponding dilatons, satisfy Generalized Supergravity Equations.

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T -folds from Yang-Baxter deformations

Cited by 48 publications

References 125 publications

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

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

Type II DFT solutions from Poisson–Lie $T$-duality/plurality

Poisson–Lie identities and dualities of Bianchi cosmologies

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