The Spacetime of Double Field Theory: Review, Remarks, and Outlook

Abstract

We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized coordinate transformations fails to associate. Moreover, in dimensional reduction, the O(d,d) T-duality transformations of fields can be obtained as generalized diffeomorphisms. Restricted to a half-dimensional subspace, DFT includes `generalized geometry', but is more general in that local patches of the doubled space may be glued together with generalized coordinate transformations. Indeed, we show that for certain T-fold backgrounds with non-geometric fluxes, there are generalized coordinate transformations that induce, as gauge symmetries of DFT, the requisite O(d,d;Z) monodromy transformations. Finally we review recent results on the α' extension of DFT which, reduced to the half-dimensional subspace, yields intriguing modifications of the basic structures of generalized geometry.

50 pages, v2: minor corrections, version to be published in Fortschritte der Physik, v3: refs. added, discussion of non-geometric backgrounds extended

References in corpus (21)

• Double Field Theory
• Generalised Geometry for M-Theory
• Double Field Theory: A Pedagogical Review
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Exceptional Form of D=11 Supergravity
• Differential geometry with a projection: Application to double field theory
• Doubled α'-Geometry
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• Double Field Theory Formulation of Heterotic Strings
• T-duality and closed string non-commutative (doubled) geometry
• Frame-like Geometry of Double Field Theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Gauge theory of Kaluza-Klein and winding modes
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Duality Symmetric String and M-Theory
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Backreacted T-folds and non-geometric regions in configuration space
• Duality Symmetry of String Theory: A Worldsheet Perspective

Cited by in corpus (200)

• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• Exceptional Field Theory III: E${}_{8(8)}$
• Search for a Higgs boson in the mass range from 145 to 1000 GeV decaying to a pair of W or Z bosons
• Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory
• Consistent Kaluza-Klein Truncations via Exceptional Field Theory
• T-duality and ${\alpha }^{\prime }$-corrections
• Entanglement, Holography and Causal Diamonds
• Double Field Theory at Order ${\alpha }^{\prime }$
• Exceptional field theory: $SL(5)$
• A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory
• Exceptional field theory: $SO(5,5)$
• Geometry and fluxes of SL(5) exceptional field theory
• Non-geometric backgrounds in string theory
• Branes are Waves and Monopoles
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Global aspects of double geometry
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• The Odd story of ${\alpha }^{\prime }$-corrections
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Half-maximal supersymmetry from exceptional field theory
• Finite Gauge Transformations and Geometry in Double Field Theory
• Double Field Theory on Group Manifolds
• Non-associative Deformations of Geometry in Double Field Theory
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• An Action for F-theory: $\mathrm{SL}(2)\times {\mathbb{R}}^{+}$ Exceptional Field Theory
• Generalized gravity from modified DFT
• The gauge structure of Exceptional Field Theories and the tensor hierarchy
• Strings and Branes are Waves
• Double Field Theory and Membrane Sigma-Models
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• The Geometry, Branes and Applications of Exceptional Field Theory
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Non-geometric branes are DFT monopoles
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• O$(d,d)$ covariant String Cosmology to all orders in ${\alpha }^{\prime }$
• String Field Theory -- A Modern Introduction
• The geometry behind double geometry
• Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds
• World-volume Effective Actions of Exotic Five-branes
• Einstein Double Field Equations
• Double Field Theory as the Double Copy of Yang-Mills
• Classical Yang-Baxter Equation from Supergravity
• Quantum correction to generalized T-dualities
• Local $\beta$-deformations and Yang-Baxter sigma model
• A new twist on heterotic string compactifications
• Gauge invariant double copy of Yang-Mills theory: the quartic theory
• Superspace with manifest T-duality from type II superstring
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• Remarks on the non-Riemannian sector in Double Field Theory
• T-duality and non-geometric solutions from double geometry
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• Second order higher-derivative corrections in Double Field Theory
• String Cosmology backgrounds from Classical String Geometry
• An O(D,D) Invariant Hamiltonian Action for the Superstring
• The rotation curve of a point particle in stringy gravity
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Dual Double Field Theory
• Generalized Dualities and Higher Derivatives
• E${}_{6(6)}$ Exceptional Field Theory: Review and Embedding of Type IIB
• Ramond-Ramond gauge fields in superspace with manifest T-duality
• Type IIB supergravity solution for the T-dual of the eta-deformed AdS_5 x S^5 superstring
• Extended Riemannian Geometry I: Local Double Field Theory
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• Double Field Theory Inspired Cosmology
• New non-perturbative de Sitter vacua in ${\alpha }^{\prime }$-complete cosmology
• Five-brane actions in double field theory
• Relating Double Field Theory to the Scalar Potential of N=2 Gauged Supergravity
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• Seeking the balance: Patching double and exceptional field theories
• Classical Yang-Baxter equation from beta-supergravity
• Hidden Gauge Structure of Supersymmetric Free Differential Algebras
• Higher Derivative Supergravities in Diverse Dimensions
• $\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• Conserved Currents of Double Field Theory
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Superstring in doubled superspace
• Triproducts, nonassociative star products and geometry of R-flux string compactifications
• Enhanced gauge symmetry and winding modes in Double Field Theory
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Sigma models for genuinely non-geometric backgrounds
• Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \textit{Twist}
• T-duality revisited
• The generalized Bergshoeff-de Roo identification II
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Looking for structure in the cobordism conjecture
• Towards a Theory of Nonassociative Gravity
• Yang-Baxter Deformation as an O(d,d) Transformation
• Symplectic realisation of electric charge in fields of monopole distributions
• Standard Model as a Double Field Theory
• Defect branes as Alice strings
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Canonical formulation and conserved charges of double field theory
• A Note on the CFT Origin of the Strong Constraint of DFT
• Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond
• From Exceptional Field Theory to Heterotic Double Field Theory via K3
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Non-Geometric F-Theory-Heterotic Duality
• Unwinding strings in semi-flatland
• Cosmological Implications from O(D,D)
• On T-duality transformations for the three-sphere
• On current algebras, generalised fluxes and non-geometry
• A note on large gauge transformations in double field theory
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Dirac structures on nilmanifolds and coexistence of fluxes
• Perturbative Double Field Theory on General Backgrounds
• Aspects of the Doubled Worldsheet
• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• ${\alpha }^{\prime }$-corrections and their double formulation
• Double field theory for the A/B-models and topological S-duality in generalized geometry
• The monodromy of T-folds and T-fects
• Type II chiral affine Lie algebras and string actions in doubled space
• Nonassociative geometry and twist deformations in non-geometric string theory
• U-gravity : $\mathbf{SL}(N)$
• Subsectors, Dynkin Diagrams and New Generalised Geometries
• New gaugings and non-geometry
• Probing the String Winding Sector
• Gravity theory on Poisson manifold with $R$-flux
• Extended Riemannian Geometry II: Local Heterotic Double Field Theory
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
• Comparing Double String Theory Actions
• Relaxing unimodularity for Yang-Baxter deformed strings
• T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
• T-duality as coordinates permutation in double space for weakly curved background
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• Currents, charges and algebras in exceptional generalised geometry
• The Asymmetric CFT Landscape in D=4,6,8 with Extended Supersymmetry
• Non-abelian fermionic T-duality in supergravity
• Global Double Field Theory is Higher Kaluza-Klein Theory
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Patching DFT, T-duality and Gerbes
• The bosonic string on string-size tori from double field theory
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
• Higher form gauge fields and their nonassociative symmetry algebras
• Towards a world-sheet description of doubled geometry in string theory
• On the phase space in Double Field Theory
• Stringy Gravity: Solving the Dark Problems at `short' distance
• Finite Transformations in Doubled and Exceptional Space
• Generalized 11D supergravity equations from tri-vector deformations
• Gauge Transformation of Double Field Theory for Open String
• A geometric formulation of exceptional field theory
• An ${\alpha }^{\prime }$-complete theory of cosmology and its tensionless limit
• Exceptional field theories, superparticles in an enlarged 11D superspace and higher spin theories
• Quantizations of D=3 Lorentz symmetry
• Partial SUSY Breaking for Asymmetric Gepner Models and Non-geometric Flux Vacua
• Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model
• Dimensional Reduction of the Generalized DBI
• New Cosmological Signatures from Double Field Theory
• Gauge symmetry enhancing-breaking from a Double Field Theory perspective
• The Algebra of Diffeomorphisms from the World Sheet
• The different faces of branes in Double Field Theory
• Twistors and supertwistors for exceptional field theory
• Deformed Weitzenböck Connections and Double Field Theory
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• Perturbative F-theory 10-brane and M-theory 5-brane
• Five-brane Current Algebras in Type II String Theories
• Double Field Theory and Geometric Quantisation
• Gravity with antisymmetric components
• O(d,d)-Duality in String Theory
• U-dualities in Type II string theories and M-theory
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• O(D,D) gauge fields in the T-dual string Lagrangian
• Finite Gauge Transformations and Geometry in Extended Field Theory
• Double Field Theory description of Heterotic gauge symmetry enhancing-breaking
• Twisted C-brackets
• On section conditions of E7(7) exceptional field theory and superparticle in N=8 central charge superspace
• Cosmological Perturbations in Double Field Theory
• Two Double String Theory Actions: Non-Covariance vs. Covariance
• Loop Corrections in Double Field Theory: Non-trivial Dilaton Potentials
• Integrability structures in string theory
• Symmetry enhancement interpolation, non-commutativity and Double Field Theory
• Non-geometric orbifolds and wrapping rules
• Effective Actions for $\sigma$-Models of Poisson-Lie Type
• Higher Spin Double Field Theory : A Proposal
• Exceptional Field Theory for $E_{6(6)}$ supergravity
• Perturbative quantum gravity in double field theory
• Gravitational Core of Double Field Theory: Lecture Notes
• Time-Dependent Warping and Non-Singular Bouncing Cosmologies
• Open-String Non-Associativity in an R-flux Background
• World-volume Effective Theories of Locally Non-geometric Branes
• The Hidden M-Group
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
• Double Field Theory on Group Manifolds in a Nutshell
• C-spaces, generalized geometry and double field theory
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Quantum Theory, Gravity and Second Order Geometry
• Gauge field fluxes and Bianchi identities in extended field theories
• Dimensional Reductions of DFT and Mirror Symmetry for Calabi-Yau Three-folds and $K3\times T^2$
• $O(d,d;\mathbb{Z})$ invariant Fierz-Pauli massive gravity
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• Double Field Theory and Pseudo-Supersymmetry
• Solutions in Exceptional Field Theory
• Instances of Higher Geometry in Field Theory
• Geometry of Membrane Sigma Models