Recent developments in non‐Abelian T‐duality in string theory

Sfetsos, Konstadinos

doi:10.1002/prop.201100063

Cited by 9 publications

(7 citation statements)

References 14 publications

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“…13) which is exactly the (homogeneous) classical Yang-Baxter equation for a bivector r on g. This proofs the conjecture, that homogeneous Yang-Baxter deformations are exactly the same as NATD β-shifts of principal chiral models.Let us also discuss the Yang-Baxter deformed model at the level of generalised fluxes.Q c ab = 0 R abc = −η 2 c 2 κ ak f k bc ,(5.14) …”

supporting

confidence: 75%

“…3. Again on a symplectic leaf of the 2-cocycle ω, which actually defines a subalgebra 13 , this defines a Poisson structure Π(g)…”

Section: Generic Casementioning

confidence: 99%

“…Non-abelian and Poisson-Lie T-duality does in general not extend to the quantum level and in some cases even spoils conformal invariance [6][7][8][9][10][11][12]. Nonetheless the study of the corresponding σ-model revealed geometric structures behind them and was also successfully used as a solution generating technique in supergravity [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality

Lüst

Osten

2018

J. High Energ. Phys.

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Based on the construction of Poisson-Lie T-dual σ-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T-duality group. This group generalises the well-known abelian T-duality group O(d, d) and we explore some of its subgroups, namely factorised dualities, B-and β-shifts. The corresponding duality transformed σ-models are constructed and interpreted as generalised (non-geometric) flux backgrounds.We also comment on generalisations of results and techniques known from abelian T-duality. This includes the Lie algebra cohomology interpretation of the corresponding non-geometric flux backgrounds, remarks on a double field theory based on non-abelian T-duality and an application to the investigation of Yang-Baxter deformations. This will show that homogeneously Yang-Baxter deformed σ-models are exactly the non-abelian T-duality β-shifts when applied to principal chiral models.This is an almost para-complex structure because J 2 = 1 and it has d-dimensional ±1eigenbundles. J is chosen in a way, that these eigenbundles are also maximally isotropic subspaces w.r.t. to | . J is integrable as its Nijenhuis-tensorThis opens a new perspective on J: Given a 2d-dimensional Lie algebra with an Ad-invariant O (d, d)-metric, then the choice of a complementary pair of maximally isotropic subspaces w.r.t. to the O(d, d)-metric defines an almost (para-)complex structure J. These subspaces are closed subalgebras, iff the almost (para-)complex structure is integrable. Thus a Manin triple decomposition (d, g, g ) can equivalently be described by the pair (d, J) with an integrable para-complex structure J.The invariance group of the integrability of J is exactly the NATD group (3.1). Non-degenerate 2-formGiven a metric | and a (para)-complex structure J it is possible to complete a compatible triple (η, J, ω J ) with a non-degenerate two-form ω J via ω J (X, Y) = J(X)|Y . (5.4) c b (∂ − g g −1 ) b .

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supporting

confidence: 75%

“…3. Again on a symplectic leaf of the 2-cocycle ω, which actually defines a subalgebra 13 , this defines a Poisson structure Π(g)…”

Section: Generic Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T -duality

Lüst

Osten

2018

J. High Energ. Phys.

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“…The result was somewhat suprising; the dual was found to be a solution of type-IIA supergravity whose lift to M-theory captures some universal properties of the solutions found by Gaiotto and Maldacena in [11], as dual geometries to the generalised N = 2 quiver SCFT's proposed by Gaiotto in [12]. Further progress and works in studying non-Abelian T-duality in this context can be found [13,14,15,16,17] and a brief review of elementary aspects of non-Abelian T-duality in [18].…”

Section: Introductionmentioning

confidence: 63%

“…The radial coordinate we now denote by τ in keeping with the notation of [21]. 18 So as to write the metric in a form compatible with our ansatz we find it convenient to introduce some functions which depend on the radial coordinate. The dictionary between the functions we use here and the original paper is as follows…”

Section: The Ks Backgroundmentioning

confidence: 99%

Non-Abelian T-duality and the AdS/CFT correspondence: New N=1 backgrounds

et al. 2013

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We consider non-Abelian T-duality on N = 1 supergravity backgrounds possessing well understood field theory duals. For the case of D3-branes at the tip of the conifold, we dualise along an SU(2) isometry. The result is a type-IIA geometry whose lift to M-theory is of the type recently proposed by Bah et. al. as the dual to certain N = 1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantised. We initiate the interpretation of these geometries in the context of AdS/CFT correspondence. We show that the central charge and the entanglement entropy are left invariant by this dualisation. The backgrounds suggest a form of Seiberg duality in the dual field theories which also exhibit domain walls and confinement in the infrared. * gitsios@upatras.gr

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