Double Field Theory: A Pedagogical Review

Abstract

Double Field Theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk-Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions, and present a brief parcours on world-sheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.

121 pages, invited review for Class. Quantum Grav; v2: Updated references

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Cited by in corpus (229)

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• Gauged Supergravities
• Entanglement, Holography and Causal Diamonds
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• A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory
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• Non-geometric backgrounds in string theory
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• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Finite Gauge Transformations and Geometry in Double Field Theory
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• Non-associative Deformations of Geometry in Double Field Theory
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
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• The gauge structure of Exceptional Field Theories and the tensor hierarchy
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• Strings and Branes are Waves
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
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• O$(d,d)$ covariant String Cosmology to all orders in ${\alpha }^{\prime }$
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• The Flux-Scaling Scenario: De Sitter Uplift and Axion Inflation
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• Einstein Double Field Equations
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• A new twist on heterotic string compactifications
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• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• Extended Riemannian Geometry I: Local Double Field Theory
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
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• Cosmological ${\alpha }^{\prime }$-corrections from the functional renormalization group
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• Higher Derivative Supergravities in Diverse Dimensions
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• From Exceptional Field Theory to Heterotic Double Field Theory via K3
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• Cosmological Implications from O(D,D)
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• Solution of the Size and Horizon Problems from Classical String Geometry
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• Type II chiral affine Lie algebras and string actions in doubled space
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• Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
• Target Space Duality of Non-Supersymmetric String Theory
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• The Asymmetric CFT Landscape in D=4,6,8 with Extended Supersymmetry
• Non-abelian fermionic T-duality in supergravity
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
• Classifying Supersymmetric Solutions in 3D Maximal Supergravity
• Towards a world-sheet description of doubled geometry in string theory
• Stringy Gravity: Solving the Dark Problems at `short' distance
• On the phase space in Double Field Theory
• The bosonic string on string-size tori from double field theory
• A Worldsheet Perspective on Heterotic T-Duality Orbifolds
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• A geometric formulation of exceptional field theory
• Generalized 11D supergravity equations from tri-vector deformations
• General relativity as a biconformal gauge theory
• Towards a classification of branes in theories with eight supercharges
• Partial SUSY Breaking for Asymmetric Gepner Models and Non-geometric Flux Vacua
• ${\alpha }^{\prime }$-corrections to DBI action via T-duality constraint
• On Missing Bianchi Identities in Cohomology Formulation
• The Magic Renormalisability of Affine Gaudin Models
• Gauge symmetry enhancing-breaking from a Double Field Theory perspective
• Classification of M2-brane 2-torus bundles, U-duality invariance and type II gauged supergravities
• Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model
• Dimensional Reduction of the Generalized DBI
• Deformed Weitzenböck Connections and Double Field Theory
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• Limitations of an Effective Field Theory Treatment of Early Universe Cosmology
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• T-duality constraint on R-R couplings
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• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
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• O(d,d)-Duality in String Theory
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
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• T-Dualities and Doubled Geometry of the Principal Chiral Model
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• Exotic Branes from del Pezzo Surfaces
• A Stringy Model of Pointlike Particles
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• Grothendieck's point of view and complexity in the black hole paradox
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Lagrangian formulation for electric charge in a magnetic monopole distribution
• Gauge field fluxes and Bianchi identities in extended field theories
• The invariant action for solitonic 5-branes
• Interactions of strings on a T-fold
• Double Field Theory for Generalized $\lambda$-deformation
• Torus Bundles, Automorphisms and T-Duality
• Double Field Theory and Pseudo-Supersymmetry
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
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• A T-Fold Black Hole in Doubled Type IIB
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• Instances of Higher Geometry in Field Theory