New Solvable Sigma Models in Plane-Parallel Wave Background

Hlavatý, Ladislav; Petr, I.

doi:10.1142/s0217751x14500092

Cited by 7 publications

(4 citation statements)

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“…Singularities of the metrics (110)-(112) are physical in the sense of [10,29], namely that they are the points of spacetime where tidal forces diverge and without them the manifold is geodesically incomplete. The metric (111) is a special case of solvable backgrounds investigated in [14,30]. The fact that this metric is T-dual of the flat metric explains its solvability.…”

Section: Discussionmentioning

confidence: 99%

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Plane-parallel waves as duals of the flat background II: T-duality with spectators

Petrasek¹,

Hlavatý²,

Petr³

2017

Class. Quantum Grav.

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We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincaré group using non-Abelian T-duality with spectators. As duals we find backgrounds for sigma models in the form of plane-parallel waves or diagonalizable curved metrics often with torsion. Among others, we find exactly solvable time-dependent isotropic pp-wave, singular ppwaves, or generalized plane wave (K-model).

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Section: Discussionmentioning

confidence: 99%

“…The metric (111) is a special case of solvable backgrounds investigated in Refs. [14,30]. The fact that this metric is T-dual of the flat metric explains its solvability.…”

mentioning

confidence: 96%

Plane-parallel waves as duals of the flat background II: T-duality with spectators

Petrasek¹,

Hlavatý²,

Petr³

2017

Class. Quantum Grav.

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“…Conventional NATD can be reproduced as a special case where one of the two groups is an Abelian group. Aspects of the PL T -duality and generalizations have been studied in [39][40][41][42][43][44][45][46][47], and concrete applications are given, for example, in [38,[48][49][50][51].Low-dimensional Drinfel'd doubles were classified in [52][53][54], and it was stressed that some Drinfel'd double d can be decomposed into several different pairs of subalgebras g andg , (d, g,g) ∼ = (d, g ′ ,g ′ ) ∼ = · · · . The decomposition is called the Manin triple, and each Manin triple corresponds to a sigma model.…”

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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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“…Sufficient condition for that is that the metrics have an isometry subgroup whose dimension is equal to the dimension of the manifold and its action on the manifold is free and transitive. This procedure was first applied for homogenous plane-parallel wave metric in [11] (see, also, [12]). On the other hand, we have lately studied the Abelian T-duality of Gödel string cosmologies up to α ′ -corrections [13] by applying the T-duality rules at two-loop order which were obtained by KM in [14].…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian T-duality of $AdS_{d\le3}$ families by Poisson-Lie T-duality

Eghbali,

Naderi,

Rezaei-Aghdam

2021

Preprint

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We proceed to investigate the non-Abelian T-duality of AdS 2 , AdS 2 × S 1 and AdS 3 physical backgrounds, as well as two-sphere S 2 from the point of view of Poisson-Lie (PL) T-duality. To this end, we reconstruct these metrics of the AdS families as backgrounds of non-linear σ-models on two-and three-dimensional Lie groups. By considering the Killing vectors of these metrics and by taking into account the fact that the subgroups of isometry Lie group of the metrics can be taken as one of the subgroups of the Drinfeld double (with Abelian duals) we look up the PL T-duality. To construct the dualizable metrics by the PL T-duality we find all subalgebras of Killing vectors that generate subgroup of isometries which acts freely and transitively on the AdS 2 , S 2 , AdS 2 × S 1 and AdS 3 manifolds. We then obtain the dual backgrounds for these families of AdS in such a way that we apply the usual rules of PL T-duality without further corrections. Meanwhile, we have shown that all original backgrounds (AdS families) are conformally invariant up to two-loop order, while this is not the case for dual solutions. Finally, by using the T-duality rules proposed by Kaloper and Meissner (KM) we calculate the Abelian T-duals of BTZ black hole up to two-loop by dualizing on the coordinates ϕ and t. In this way, only the corresponding dual metrics and dilaton fields receive α ′ -corrections. When the dualizing is implemented by the shift of direction ϕ, we show that the horizons and singularity of the dual spacetime are the same as in charged black string derived by Horne and Horowitz without α ′ -corrections, whereas in dualizing on the coordinate t we find a new three-dimensional black string whose structure and asymptotic nature are clearly determined. For this case, we show that the Abelian T-duality transformation of KM changes the asymptotic behavior from AdS 3 to flat.

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New Solvable Sigma Models in Plane-Parallel Wave Background

Cited by 7 publications

References 20 publications

Plane-parallel waves as duals of the flat background II: T-duality with spectators

Plane-parallel waves as duals of the flat background II: T-duality with spectators

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

Non-Abelian T-duality of $AdS_{d\le3}$ families by Poisson-Lie T-duality

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