Nonabelian Dualization of Plane Wave Backgrounds

Hlavatý, Ladislav; Turek, Miroslav

doi:10.4236/jmp.2012.39143

Cited by 5 publications

(12 citation statements)

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“…The existence of several decompositions suggests that many sigma models are related through a Drinfel'd double. This idea was explicitly realized in [55] and the classical equivalence of the sigma models was called the PL T -plurality (see 2 [56][57][58][59][60] for more examples). Various aspects of the PL T -plurality were discussed in [61,62] and in particular quantum aspects of the PL T -duality/plurality were studied in [55,[63][64][65][66][67][68][69][70][71].Recent developments in NATD were triggered by [72], which provided the transformation rule for the R-R fields under NATD.…”

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

Sakatani

2019

Progress of Theoretical and Experimental Physics

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“…As explained in section 2, dualizable metrics are constructed by virtue of the Drinfeld double. To get the metric (15), the Lie algebra of the Drinfeld double can be composed from the four-dimensional Lie subalgebra of the isometry algebra of Killing vectors (20) and four-dimensional Abelian algebra 2 . Moreover, the four-dimensional subgroup of isometries must act freely and transitively [11] on the Riemannian manifold M where the metric is defined, so that M ≈ G. These four-dimensional subgroups were found in [15] as…”

Section: Data For Construction Of Dual Backgroundsmentioning

confidence: 99%

“…In the following we shall find metrics dual to (15) constructed from the Drinfeld doubles d = g ⊕ a where g is g 1 or g 2 and a is four-dimensional Abelian algebra.…”

Section: Data For Construction Of Dual Backgroundsmentioning

confidence: 99%

“…The transformation between group coordinates x 1 , x 2 , x 3 , x 4 defined by (37) and geometrical coordinates u, v, x, y on M can be obtained by comparing the left-invariant vector fields on the group G and Killing vectors of the metric (15). One gets…”

Section: Data For Construction Of Dual Backgroundsmentioning

confidence: 99%

“…Even though it is not symmetric, its torsion is zero. It satisfies the conformal invariance conditions (16)- (18) with the dilaton field [15] Φ =Φ 0 + C ln x 1 − 1…”

Section: Data For Construction Of Dual Backgroundsmentioning

confidence: 99%

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New Solvable Sigma Models in Plane-Parallel Wave Background

Hlavatý

Petr

2014

Int. J. Mod. Phys. A

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We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-abelian Drinfeld doubles are used which contain the isometry group of the homogeneous plane wave metric. The dual solutions are then found by the Poisson-Lie transformation of the explicit solution of the original homogeneous plane wave background. Investigating their Killing vectors, we have found that the dual backgrounds can be transformed to the form of more general plane-parallel waves.

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Non-Abelian U -duality for membranes

Sakatani

Uehara

2020

Progress of Theoretical and Experimental Physics

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Abstract The $T$-duality of string theory can be extended to the Poisson–Lie $T$-duality when the target space has a generalized isometry group given by a Drinfel’d double. In M-theory, $T$-duality is understood as a subgroup of $U$-duality, but the non-Abelian extension of $U$-duality is still a mystery. In this paper we study membrane theory on a curved background with a generalized isometry group given by the $\mathcal E_n$ algebra. This provides a natural setup to study non-Abelian $U$-duality because the $\mathcal E_n$ algebra has been proposed as a $U$-duality extension of the Drinfel’d double. We show that the standard treatment of Abelian $U$-duality can be extended to the non-Abelian setup. However, a famous issue in Abelian $U$-duality still exists in the non-Abelian extension.

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Nonabelian Dualization of Plane Wave Backgrounds

Cited by 5 publications

References 8 publications

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

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

New Solvable Sigma Models in Plane-Parallel Wave Background

Non-Abelian U -duality for membranes

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