Non‐abelian T‐duality of Pilch‐Warner background

Dimov, H.; Mladenov, Stefan; Rashkov, R. C.; Vetsov, T.

doi:10.1002/prop.201600032

Cited by 14 publications

(17 citation statements)

References 58 publications

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“…We also note that the approach of [80] based on the Fourier-Mukai transformation (see also [96] for an application) will be closely related to the procedure explained here.…”

Section: R-r Fields As a Polyformmentioning

confidence: 95%

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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“…We also note that the approach of [80] based on the Fourier-Mukai transformation (see also [96] for an application) will be closely related to the procedure explained here.…”

Section: R-r Fields As a Polyformmentioning

confidence: 95%

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

Sakatani

2019

Progress of Theoretical and Experimental Physics

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“…Beyond conformal field theories one can also find supergravity solutions that encode rich RG dynamics of the QFT. This was achieved [41,90] by using the Klebanov-Strassler geometry as a seed solution to non-Abelian T-duality, or other RG flows like the Plich-Warner [87,91], and eventually paved the way for construction of backgrounds that geometrically encode confinement [85] in terms of an internal manifold with a dynamic SU(2) structure.…”

Section: Seed Solutionmentioning

confidence: 99%

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Thompson¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application in the context of holography. Non-Abelian T-duality has been used to construct new holographic dual geometries. Poisson-Lie duality has been used to construct new integrable string sigma-models including the η-and λ -deformations of the AdS 5 × S 5 superstring thought to encode quantum group deformations of holography. We also comment on the doubled worldsheet description that makes such dualities manifest. duality serves to interchange a conservation law, that associated to the U(1) global symmetry of the compact boson θ of radius R, with the Bianchi identity for the dual bosonθ :( 1.3) Just as with bosonisation the connection between the two variables involves derivatives, i.e. the map between variables is a non-local one. Also akin to the Abelian bosonisation, the dual theory can be established through an analogous path integral manipulation 1 known as the Buscher procedure [22,23]. Given the close analogy between T-duality and Abelian bosonisation one might wonder if there is a T-duality equivalent to non-Abelian bosonisation. More specifically, in string theory we are immediately prompted to ask if there is an extension of T-duality to the case of a non-Abelian set of isometries, or even if there are still more exotic notions of T-duality? A secondary question is then, if such dualities exist, what are they useful for? The remainder of these lectures seek to outline some answers to these two questions.Our journey will involve exploring a hierarchy of possible dualities in the following string theory scenarios:

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“…De la Ossa and Quevedo generalised the gauging procedure of Buscher to extend the technique to spaces admitting a non-abelian group of isometries [15], and this was later extended to include the Ramond-Ramond fields [40,31]. Although the role that nonabelian T-duality plays in string theory is currently unclear, it has been employed successfully as a solution generating technique in supergravity [1,2,12,16,24,30,35,36,38,41] and generalised supergravity [20]. It has also been studied in the context of the AdS/CFT correspondence in [17,18,23,26,27,28].…”

Section: Introductionmentioning

confidence: 99%