Non-geometric backgrounds, doubled geometry and generalised T-duality

Abstract

String backgrounds with a local torus fibration such as T-folds are naturally formulated in a doubled formalism in which the torus fibres are doubled to include dual coordinates conjugate to winding number. Here we formulate and explore a generalisation of this construction in which all coordinates are doubled, so that the doubled space is a twisted torus, i.e. a compact space constructed from identifying a group manifold under a discrete subgroup. This incorporates reductions with duality twists, T-folds and a class of flux compactifications, together with the non-geometric backgrounds expected to arise from these through T-duality. It also incorporates backgrounds that are not even locally geometric, and suggests a generalisation of T-duality to a more general context. We discuss the effective field theory arising from such an internal sector, give a world-sheet sigma model formulation of string theory on such backgrounds and illustrate our discussion with detailed examples.

81 pages

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Cited by in corpus (99)

• Double Field Theory
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• Exploring Double Field Theory
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• Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions
• T-duality and closed string non-commutative (doubled) geometry
• Exotic Branes in String Theory
• The effective action of Double Field Theory
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Geometry and fluxes of SL(5) exceptional field theory
• Doubled aspects of generalised dualities and integrable deformations
• Non-geometric backgrounds in string theory
• The O_{D,D} Geometry of String Theory
• Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions
• Half-maximal supersymmetry from exceptional field theory
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Finite Gauge Transformations and Geometry in Double Field Theory
• Double Field Theory on Group Manifolds
• Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• Duality Symmetric String and M-Theory
• Effective actions of non-geometric fivebranes
• Connecting T-duality invariant theories
• The KK-Monopole/NS5-Brane in Doubled Geometry
• Double Field Theory and Membrane Sigma-Models
• A Double Sigma Model for Double Field Theory
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Non-geometric branes are DFT monopoles
• Conformal chiral boson models on twisted doubled tori and non-geometric string vacua
• The Revival of (0,2) Linear Sigma Models
• Matrix theory origins of non-geometric fluxes
• Double Field Theory for Double D-branes
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• D-branes and doubled geometry
• Exceptional Flux Compactifications
• An O(D,D) Invariant Hamiltonian Action for the Superstring
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• Extended Riemannian Geometry I: Local Double Field Theory
• T-folds, doubled geometry, and the SU(2) WZW model
• T-Dual Cosmological Solutions of Double Field Theory II
• T-dual cosmological solutions in double field theory
• Exploring Exceptional Drinfeld Geometries
• A Lorentz invariant doubled worldsheet theory
• Sigma models for genuinely non-geometric backgrounds
• Unwinding strings in semi-flatland
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• Dirac structures on nilmanifolds and coexistence of fluxes
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• Generalized Parallelizable Spaces from Exceptional Field Theory
• Doubling, T-Duality and Generalized Geometry: a Simple Model
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• New gaugings and non-geometry
• Extended Riemannian Geometry II: Local Heterotic Double Field Theory
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• Semi-doubled Sigma Models for Five-branes
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• Global Double Field Theory is Higher Kaluza-Klein Theory
• U-duality in three and four dimensions
• Closed String Partition Functions in Toroidal Compactifications of Doubled Geometries
• Topological T-Duality for Twisted Tori
• T-dualization of type II superstring theory in double space
• Dilogarithms, OPE and twisted T-duality
• Bi-algebras, generalised geometry and T-duality
• Stringy Newton Gravity with $H$-flux
• Extended Riemannian Geometry III: Global Double Field Theory with Nilmanifolds
• Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• Black holes in string theory with duality twists
• Degenerations of K3, Orientifolds and Exotic Branes
• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
• The Doubled Geometry of Nilmanifold Reductions
• Para-hyperhermitian surfaces
• A Simple Model of Double Dynamics on Lie Groups
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Gauged Supergravities and the Physics of Extra Dimensions
• Poisson-Lie T-plurality for dressing cosets
• Special Holonomy Manifolds, Domain Walls, Intersecting Branes and T-folds
• Advantage of the second-order formalism in double space T-dualization of type II superstring
• Heterotic type IIA duality with fluxes - towards the complete story
• Open-String Non-Associativity in an R-flux Background
• 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
• String theory in twistor space and minimal tension holography
• Renormalization of a Lorentz invariant doubled worldsheet theory
• Lagrangian formulation for electric charge in a magnetic monopole distribution
• Torus Bundles, Automorphisms and T-Duality
• Double Field Theory for Generalized $\lambda$-deformation
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Minkowski vacuum transitions in (non-geometric) flux compactifications
• Gaugings and other aspects in supergravity
• Double space T-dualization and coordinate dependent RR
• Extended Field Theories as higher Kaluza-Klein theories
• Non-geometric fluxes and mixed-symmetry potentials