The Algebroid Structure of Double Field Theory

Chatzistavrakidis, Athanasios; Jonke, Larisa; Khoo, Fech Scen; Szabo, Richard J.

doi:10.22323/1.347.0132

Cited by 6 publications

(2 citation statements)

References 30 publications

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“…Note that the DFT geometry is still not fully understood in the mathematical literature, and although it recovers Riemannian backgrounds under certain conditions, it is certainly much more general, see e.g. [30,[63][64][65][66][67][68][69][70][71][72][73][74][75][76][77]. The geometrical framework of DFT allows us to define a generalization of the scalar and Ricci curvatures, S (0) and P A CP B D S C D [78] (c.f.…”

Section: The O( D D) Paradigm: Review Of the Einstein Double Field Equationsmentioning

confidence: 99%

$$\mathbf {O}(D,D)$$ completion of the Friedmann equations

et al. 2020

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In string theory the closed-string massless NS-NS sector forms a multiplet of $$\mathbf {O}(D,D)$$ O ( D , D ) symmetry. This suggests a specific modification to General Relativity in which the entire NS-NS sector is promoted to stringy graviton fields. Imposing off-shell $$\mathbf {O}(D,D)$$ O ( D , D ) symmetry fixes the correct couplings to other matter fields and the Einstein field equations are enriched to comprise $$D^{2}+1$$ D 2 + 1 components, dubbed recently as the Einstein Double Field Equations. Here we explore the cosmological implications of this framework. We derive the most general homogeneous and isotropic ansatzes for both stringy graviton fields and the $$\mathbf {O}(D,D)$$ O ( D , D ) -covariant energy-momentum tensor. Crucially, the former admits space-filling magnetic H-flux. Substituting them into the Einstein Double Field Equations, we obtain the $$\mathbf {O}(D,D)$$ O ( D , D ) completion of the Friedmann equations along with a generalized continuity equation. We discuss how solutions in this framework may be characterized by two equation-of-state parameters, w and $$\lambda $$ λ , where the latter characterizes the relative intensities of scalar and tensor forces. When $$\lambda +3w=1$$ λ + 3 w = 1 , the dilaton remains constant throughout the cosmological evolution, and one recovers the standard Friedmann equations for generic matter content (i.e. for any w). We further point out that, in contrast to General Relativity, neither an $$\mathbf {O}(D,D)$$ O ( D , D ) -symmetric cosmological constant nor a scalar field with positive energy density gives rise to a de Sitter solution.

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Section: The O( D D) Paradigm: Review Of the Einstein Double Field Equationsmentioning

confidence: 99%

$$\mathbf {O}(D,D)$$ completion of the Friedmann equations

et al. 2020

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“…Over the years, DFT has shown interesting and deep connections to various subfields of geometry, such as Generalized Geometry [40][41][42][43][44][45], Courant algebroid (including extensions thereof) [46][47][48], and para-Hermitian/Born geometry [49][50][51][52][53][54][55][56][57][58]. More recently, graded geometry has been also used to describe the symmetries of DFT [59][60][61][62][63][64][65][66] (making, in particular, use of derived brackets introduced in [67] and further studied in [68][69][70][71]).…”

Section: Introductionmentioning

confidence: 99%

A note on Faddeev-Popov action for doubled-yet-gauged particle and graded Poisson geometry

Basile

Joung

Park

2020

J. High Energ. Phys.

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The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev-Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which are analogous to the Fradkin-Tseytlin term on string worldsheet. arXiv:1910.13120v1 [hep-th] 29 Oct 2019 to DFT. Section 2 contains our main results which split into three parts. Firstly, we introduce a constant projector into a section, and using this we reformulate the section condition as well as the coordinate gauge symmetry. Secondly, we consider the BRST formulation of the doubled-yet-gauged particle action [33], and point out its connection to the graded Poisson geometry [62,63]. Thirdly, by requiring target space-

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O(d,d) covariant formulation of Type II supergravity and Scherk-Schwarz reduction

Çatal-Özer

2022

J. Phys.: Conf. Ser.

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T-duality is a stringy symmetry which relates string backgrounds with different space-time geometries. In the low energy limit, it manifests itself as a continuous O(d,d) symmetry acting on supergravity fields, after dimensional reduction on a d dimensional torus. Double Field Theory (DFT) is a T-duality covariant extension of string theory which aims to realize O(d,d) as a manifest symmetry for the low energy effective space-time actions of string theory without dimensional reduction. The mathematical framework needed to construct DFT goes beyond Riemannian geometry and is related to Hitchin’s generalized geometry program. On the other hand, Scherk-Schwarz reduction of DFT of Type II strings with a duality twist in O(d,d) yields Gauged Double Field Theory (GDFT), that can be regarded as an O(d,d) covariant extension of gauged supergravity. The purpose of this contribution is to give a short review on Scherk-Schwarz reductions of DFT and its intriguing connections to integrable deformations of string sigma models.

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The Algebroid Structure of Double Field Theory

Cited by 6 publications

References 30 publications

$$\mathbf {O}(D,D)$$ completion of the Friedmann equations

$$\mathbf {O}(D,D)$$ completion of the Friedmann equations

A note on Faddeev-Popov action for doubled-yet-gauged particle and graded Poisson geometry

O(d,d) covariant formulation of Type II supergravity and Scherk-Schwarz reduction

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