Kaluza–Klein reduction on a maximally non-Riemannian space is moduli-free

Cho, Kyoungho; Morand, Kevin; Park, Jeong-Hyuck

doi:10.1016/j.physletb.2019.04.042

Cited by 20 publications

(24 citation statements)

References 78 publications

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“…This type of (genuinely) DFT solution is called the non-Riemannian background [167], and is studied in detail in [168][169][170][171]. Using a parameterization given in [169], we find that…”

Section: Ads 3 × S 3 × T 4 : Examplementioning

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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Section: Ads 3 × S 3 × T 4 : Examplementioning

confidence: 99%

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

Sakatani

2019

Progress of Theoretical and Experimental Physics

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“…[35] for a short summary): [14], while T AB is the on-shell conserved energy-momentum tensor, defined through the variation of the matter Lagrangian with respect to {H AB , d} [15]. Remarkably, the perfectly O(D, D)-symmetric vacua, satisfying G AB = 0, turned out to be a topological phase which allows no moduli and no interpretation within Riemannian geometry, thus escaping beyond the realm of GR [30,36,37]. Only after a spontaneous symmetry breaking of O(D, D), the familiar string theory backgrounds characterized by the Riemannian metric g µν and the Kalb-Ramond skew-symmetric two-form potential B µν emerge: these component fields parametrize the DFT-metric while being identified as the Nambu-Goldstone bosons [38].…”

Section: Introductionmentioning

confidence: 99%

Stringy Newton gravity with H -flux

2020

Self Cite

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A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity:Not only the mass density ρ but also the current density K is intrinsic to matter. Sourcing H which is of NS-NS H-flux origin, K is nontrivial if the matter is 'stringy'. H contributes quadratically to the Newton potential, but otherwise is decoupled from the point particle dynamics, i.e.ẍ = −∇Φ. We define 'stringization' analogous to magnetization and discuss regular as well as monopole-like singular solutions.

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“…However, pure DFT itself cannot be a consistent low energy effective field theory of the string because of anomaly issues. Additional Yang-Mills gauge fields or Ramond-Ramond fields must be coupled to pure DFT to make a consistent theory.In the present paper, we extend the KS formalism for pure DFT to the heterotic DFT [40, 41] (see also [42] for the non-Riemannian origin). Heterotic DFT incorporates Yang-Mills gauge theory into pure DFT in a duality covariant manner, and it is described in terms of the O(d, d + G) gauged DFT, where G represents the dimension of the Yang-Mills gauge group 1 .…”

mentioning

confidence: 99%

“…In the present paper, we extend the KS formalism for pure DFT to the heterotic DFT [40, 41] (see also [42] for the non-Riemannian origin). Heterotic DFT incorporates Yang-Mills gauge theory into pure DFT in a duality covariant manner, and it is described in terms of the O(d, d + G) gauged DFT, where G represents the dimension of the Yang-Mills gauge group 1 .…”

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confidence: 99%

Heterotic Kerr-Schild double field theory and classical double copy

Cho

Lee

2019

J. High Energ. Phys.

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We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O (d, d + G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of motion under the heterotic KS ansatz in a flat background can be reduced to linear equations. Using the heterotic KS equations, we establish the single and zeroth copy for heterotic supergravity and derive the Maxwell and Maxwell-scalar equations. This agrees with the KLT relation for heterotic string theory.1 O (1, d − 1) structure groups. It inherits from the left-right sector decomposition of the closed string, and each O (1, d − 1) group corresponds to the local Lorentz group of the target spacetime seen by the left and right sectors respectively. Since the double copy and KLT relations are also closely related to the left-right decomposition of the closed string, DFT provides a useful tool for describing such a hidden structure [38,39].The KS ansatz for pure DFT, which consists of the massless NS-NS sector only, is constructed in terms of a pair of null O (d, d) vectors [27]. The corresponding equations of motion can be reduced to linear equations by restricting the DFT dilaton appropriately. Based on this formalism, the classical double copy is extended to the entire massless NS-NS sector, and two independent Maxwell equations are derived from the KS equations. However, pure DFT itself cannot be a consistent low energy effective field theory of the string because of anomaly issues. Additional Yang-Mills gauge fields or Ramond-Ramond fields must be coupled to pure DFT to make a consistent theory.In the present paper, we extend the KS formalism for pure DFT to the heterotic DFT [40, 41] (see also [42] for the non-Riemannian origin). Heterotic DFT incorporates Yang-Mills gauge theory into pure DFT in a duality covariant manner, and it is described in terms of the O(d, d + G) gauged DFT, where G represents the dimension of the Yang-Mills gauge group 1 . The heterotic KS ansatz for the generalized metric is the same form as in the pure DFT case and written in terms of a pair of O (d, d + G) null vectors. However, its d-dimensional supergravity representations are quite different. One of the remarkable properties of the heterotic KS ansatz is that the null condition can be partially relaxed in the d-dimensional language while preserving the linearity of the field equations. We obtain the on-shell constraint for the O (d, d+ G) null vectors and DFT dilaton, which corresponds to the geodesic condition in the usual KS formalism in GR. Using the null and on-shell constraints together, the field equations under the heterotic...

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Kaluza–Klein reduction on a maximally non-Riemannian space is moduli-free

Cited by 20 publications

References 78 publications

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

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

Stringy Newton gravity with H -flux

Heterotic Kerr-Schild double field theory and classical double copy

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