Non-geometric backgrounds in string theory

Abstract

This review provides an introduction to non-geometric backgrounds in string theory. Starting from a discussion of T-duality, geometric and non-geometric torus-fibrations are reviewed, generalised geometry and its relation to non-geometric backgrounds are explained and compactifications of string theory with geometric and non-geometric fluxes are discussed. Furthermore covered are doubled geometry as well as non-commutative and non-associative structures in the context of non-geometric backgrounds.

arXiv commentPublished in Physics Reports; 249 pages; v2: references added, new section 3.4, other minor changes; v3: published version, typos fixed

References in corpus (288)

• The Large N Limit of Superconformal Field Theories and Supergravity
• String Theory and Noncommutative Geometry
• de Sitter Vacua in String Theory
• String Theory Dynamics In Various Dimensions
• Quantum Field Theory on Noncommutative Spaces
• Unity of Superstring Dualities
• Evidence for F-Theory
• Supergravity description of field theories on curved manifolds and a no go theorem
• Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications
• CFT's From Calabi-Yau Four-folds
• Target Space Duality in String Theory
• M Theory, Orientifolds and G-Flux
• Mirror Symmetry is T-Duality
• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Double Field Theory
• Flux Compactification
• Flux compactifications in string theory: a comprehensive review
• Distance and de Sitter Conjectures on the Swampland
• Super-Poincare Covariant Quantization of the Superstring
• Generalized metric formulation of double field theory
• Branes Intersecting at Angles
• Superspace Duality in Low-Energy Superstrings
• Noncommutative Open String and D-brane
• A Geometry for Non-Geometric String Backgrounds
• D-branes and the Noncommutative Torus
• D-branes and Deformation Quantization
• Duality in the Type--II Superstring Effective Action
• Noncompact Symmetries in String Theory
• Duality, Quotients, and Currents
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
• Background independent action for double field theory
• The effective action of N=1 Calabi-Yau orientifolds
• Nongeometric Flux Compactifications
• Duality Symmetries from Non--Abelian Isometries in String Theories
• U-duality and M-Theory
• Duality of Type II 7-branes and 8-branes
• New Supersymmetric String Compactifications
• Dual Non-Abelian Duality and the Drinfeld Double
• Self-duality of Born-Infeld action and Dirichlet 3-brane of type IIB superstring theory
• Noncommutative Compactifications of Type I Strings on Tori with Magnetic Background Flux
• K-theory and Ramond-Ramond charge
• Doubled Geometry and T-Folds
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Dualisation of Dualities, I
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• Generalized structures of N=1 vacua
• Double Field Theory: A Pedagogical Review
• On Lorentz Invariant Actions for Chiral P-Forms
• The effective action of Type IIA Calabi-Yau orientifolds
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Noncommutative Geometry From Strings and Branes
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Duality Twists, Orbifolds, and Fluxes
• Generalized Geometry and M theory
• Supergravity as Generalised Geometry I: Type II Theories
• Some Global Aspects of Duality is String Theory
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold
• An Sl(2,Z) Multiplet of Nine-Dimensional Type II Supergravity Theories
• A scan for new N=1 vacua on twisted tori
• Geometric Constructions of Nongeometric String Theories
• Exceptional Field Theory I: $E_{6(6)}$ covariant Form of M-Theory and Type IIB
• The O(dd) Story of Massive Supergravity
• Duality and Dilaton
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Double Field Theory and N=4 Gauged Supergravity
• Partial breaking of global D=4 supersymmetry, constrained superfields, and 3-brane actions
• Exceptional Field Theory III: E${}_{8(8)}$
• Exploring Double Field Theory
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• NS5-Branes, T-Duality and Worldsheet Instantons
• On non-abelian T-dual geometries with Ramond fluxes
• T-Duality, Space-time Spinors and R-R Fields in Curved Backgrounds
• Lectures on Gauged Supergravity and Flux Compactifications
• Derived brackets
• Summing up D-Instantons
• Poisson-Lie T-duality
• Exceptional Field Theory II: E${}_{7(7)}$
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• Inflationary Constraints on Type IIA String Theory
• Hitchin Functionals in N=2 Supergravity
• Generalised T-Duality and Non-Geometric Backgrounds
• Type II Theories Compactified on Calabi-Yau Threefolds in the Presence of Background Fluxes
• On Nonabelian Duality
• Symplectic structures associated to Lie-Poisson groups
• On Non-Abelian Duality
• Compactifications of Type IIB Strings to Four Dimensions with Non-trivial Classical Potential
• More Dual Fluxes and Moduli Fixing
• Generalized Duality in Curved String-Backgrounds
• Gauged Double Field Theory
• A ten-dimensional action for non-geometric fluxes
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• T-Duality: Topology Change from H-flux
• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• T-duality for torus bundles via noncommutative topology
• A Canonical Approach to Duality Transformations
• Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory
• Currents, Charges, and Canonical Structure of Pseudodual Chiral Models
• Supersymmetric AdS_6 via T-duality
• D-brane Wess--Zumino actions, T-duality and the cosmological constant
• T-duality and closed string non-commutative (doubled) geometry
• A geometric action for non-geometric fluxes
• Nonassociative Gravity in String Theory?
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Exotic Branes in String Theory
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Lectures on Generalized Complex Geometry for Physicists
• Exotic branes and non-geometric backgrounds
• Abelian Yang-Baxter Deformations and TsT transformations
• D-branes and T-duality
• Generalized Flux Vacua
• Nonassociative tori and applications to T-duality
• Magnetic charges in local field theory
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Open Strings and D-branes in WZNW model
• Constructing Nongeometric Vacua in String Theory
• Gauged Supergravities
• Spacetimes for λ-deformations
• Exact Duality Symmetries in CFT and String Theory
• Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• Flux moduli stabilisation, Supergravity algebras and no-go theorems
• Background Field Equations for the Duality Symmetric String
• Current Algebras and Differential Geometry
• Type IIB supergravity compactified on a Calabi-Yau manifold with H-fluxes
• T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Torsional Heterotic Geometries
• Gauged WZW models and Non-abelian duality
• Charting the landscape of N=4 flux compactifications
• On the distribution of stable de Sitter vacua
• D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications
• Frame-like Geometry of Double Field Theory
• Complete classification of Minkowski vacua in generalised flux models
• Lattice Wess-Zumino-Witten Model and Quantum Groups
• Compactification of Type IIB String Theory on Calabi-Yau Threefolds
• Lectures on Nongeometric Flux Compactifications
• Non-Abelian Duality and Canonical Transformations
• A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Comments on double field theory and diffeomorphisms
• Geometry and fluxes of SL(5) exceptional field theory
• 5-branes, KK-monopoles and T-duality
• Generalised $G_2$-structures and type IIB superstrings
• U-Manifolds
• β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
• Massive String Theories From M-Theory and F-Theory
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Flux Compactifications of M-Theory on Twisted Tori
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Non-Abelian T-duality and consistent truncations in type-II supergravity
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• T-duality for principal torus bundles
• Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• SO(d,d) Transformations of Ramond-Ramond Fields and Space-time Spinors
• Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
• Towards Minkowski Vacua in Type II String Compactifications
• T-duality for open strings
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• On Non-Abelian T-Duality and new N=1 backgrounds
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• Gauge Symmetry, T-Duality and Doubled Geometry
• Flux Compactifications of String Theory on Twisted Tori
• 7-Branes and Higher Kaluza-Klein Branes
• Seven-branes and Supersymmetry
• Non-associative Deformations of Geometry in Double Field Theory
• Toroidal Orientifolds in IIA with General NS-NS Fluxes
• 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
• The Scherk-Schwarz mechanism as a flux compactification with internal torsion
• Towards Axionic Starobinsky-like Inflation in String Theory
• Slow-Roll Inflation in Non-geometric Flux Compactification
• Worldsheet Instanton Corrections to 522-brane Geometry
• Effective actions of non-geometric fivebranes
• (Non-)commutative closed string on T-dual toroidal backgrounds
• More stable dS vacua from S-dual non-geometric fluxes
• Gauged Linear Sigma Model for Exotic Five-brane
• The KK-Monopole/NS5-Brane in Doubled Geometry
• Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry
• Double Field Theory and Membrane Sigma-Models
• Poisson-Lie T-Duality: the Path-Integral Derivation
• Quantum Poisson-Lie T-duality and WZNW model
• Classification of 6-dimensional real Drinfeld doubles
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids
• Renormalization of Lorentz non-invariant actions and manifest T-duality
• On Type IIB moduli stabilization and N = 4, 8 supergravities
• Counting supersymmetric branes
• On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
• $T$-folds from Yang-Baxter deformations
• Conformal chiral boson models on twisted doubled tori and non-geometric string vacua
• T-duality with H-flux: non-commutativity, T-folds and G x G structure
• Flux Compactifications, Gauge Algebras and De Sitter
• Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory
• Algebras and non-geometric flux vacua
• Branes and wrapping rules
• The Flux-Scaling Scenario: De Sitter Uplift and Axion Inflation
• Massive IIA String Theory and Matrix Theory Compactification
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• The Intriguing Structure of Non-geometric Frames in String Theory
• Nongeometry, Duality Twists, and the Worldsheet
• Matrix theory origins of non-geometric fluxes
• Duality and Canonical Transformations
• On T-duality for open strings in general abelian and nonabelian gauge field backgrounds
• Poisson-Lie T-duality and Courant algebroids
• Poisson-Lie T-Duality and Bianchi Type Algebras
• Star Products from Open Strings in Curved Backgrounds
• Non-geometric String Backgrounds and Worldsheet Algebras
• Non-geometric flux vacua, S-duality and algebraic geometry
• Aspects of T-duality in Open Strings
• Low Energy Supersymmetry from Non-Geometry
• NS-NS fluxes in Hitchin's generalized geometry
• T-duality in Ramond-Ramond backgrounds
• Poisson-Lie T-duality: Open Strings and D-branes
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• De Sitter Vacua from Non-perturbative Flux Compactifications
• The Generalized Green-Schwarz Mechanism for Type IIB Orientifolds with D3- and D7-Branes
• The N=1 Low-Energy Effective Action of Spontaneously Broken N=2 Supergravities
• Reducing democratic type II supergravity on SU(3) x SU(3) structures
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• A special road to AdS vacua
• Marginal and non-commutative deformations via non-abelian T-duality
• Type IIB flux vacua from G-theory II
• Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
• Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry
• T-duality of the Green-Schwarz superstring
• Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
• Branes, U-folds and hyperelliptic fibrations
• Nonassociative differential geometry and gravity with non-geometric fluxes
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• On general flux backgrounds with localized sources
• A Lorentz invariant doubled worldsheet theory
• Worldsheet theories for non-geometric string backgrounds
• Triproducts, nonassociative star products and geometry of R-flux string compactifications
• Type IIB flux vacua from G-theory I
• Heterotic T-fects, 6D SCFTs, and F-Theory
• T-duality revisited
• Sigma models for genuinely non-geometric backgrounds
• Effective descriptions of branes on non-geometric tori
• Canonical pure spinor (Fermionic) T-duality
• Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization
• Semi-Flatland
• Towards a Theory of Nonassociative Gravity
• Geometry and Duality in Supersymmetric sigma-Models
• Mirrorfolds with K3 Fibrations
• U-branes and T^3 fibrations
• Exotic branes in Exceptional Field Theory: the SL(5) duality group
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
• Non-Geometric F-Theory-Heterotic Duality
• On T-duality transformations for the three-sphere
• Unwinding strings in semi-flatland
• Nonassociative Weyl star products
• Non-geometric Calabi-Yau Backgrounds and K3 automorphisms
• Asymmetric Gepner models in type II
• Non-Abelian Duality for Open Strings
• States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution
• Examples of N=2 to N=1 supersymmetry breaking
• Testing non-associative quantum mechanics
• Aspects of the Doubled Worldsheet
• Abelian duality in WZW models
• On T-folds, G-structures and Supersymmetry
• The monodromy of T-folds and T-fects
• Locally non-geometric fluxes and missing momenta in M-theory
• Backreacted T-folds and non-geometric regions in configuration space
• T-duality Twists and Asymmetric Orbifolds
• Non-geometric Kaluza-Klein monopoles and magnetic duals of M-theory R-flux backgrounds
• Freed-Witten anomaly in general flux compactification
• Patching DFT, T-duality and Gerbes
• Towards a world-sheet description of doubled geometry in string theory
• U-dual branes and mixed symmetry tensor fields
• T-duality for the sigma model with boundaries
• Non-geometric Calabi-Yau compactifications and fractional mirror symmetry
• Weak associativity and deformation quantization
• Small magnetic charges and monopoles in non-associative quantum mechanics
• Partial SUSY Breaking for Asymmetric Gepner Models and Non-geometric Flux Vacua
• Monopole star products are non-alternative
• Non-geometric Five-branes in Heterotic Supergravity
• Open-string T-duality and applications to non-geometric backgrounds
• Poisson-Lie T-plurality as canonical transformation
• Lie algebroids, non-associative structures and non-geometric fluxes
• T-duality transformations for the NS5-brane along angular directions

Cited by in corpus (58)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Remarks on the non-Riemannian sector in Double Field Theory
• Unitarization from Geometry
• Quintessence and the Swampland: The numerically controlled regime of moduli space
• A master exceptional field theory
• Non-Riemannian geometry of M-theory
• Systematics of type IIB moduli stabilisation with odd axions
• Systematics of Type IIA moduli stabilisation
• Type IIB flux vacua and tadpole cancellation
• The Holographic Conformal Manifold of 3d $\mathcal{N}=2$ $S$-fold SCFTs
• Mass spectrum of type IIB flux compactifications -- comments on AdS vacua and conformal dimensions
• Resolving spacetime singularities in flux compactifications & KKLT
• Looking for structure in the cobordism conjecture
• Dictionary for the type II nongeometric flux compactifications
• Moduli stabilization in type IIB orientifolds at $h^{2,1}=50$
• On current algebras, generalised fluxes and non-geometry
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
• Rigid nongeometric orientifolds and the swampland
• Democratic actions for type II supergravities
• The $\beta$-symmetry of supergravity
• Moduli stabilization with non-geometric fluxes -- comments on tadpole contributions and de-Sitter vacua
• $O(d,d)$ transformations preserve classical integrability
• de Sitter Minima from M theory and String theory
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Classical de Sitter solutions in three dimensions without tachyons?
• On stable type IIA de-Sitter vacua with geometric flux
• Currents, charges and algebras in exceptional generalised geometry
• Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• Towards Classification of $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ Asymmetric ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ Heterotic String Orbifolds
• Degenerations of K3, Orientifolds and Exotic Branes
• Courant bracket twisted both by a 2-form $B$ and by a bi-vector $\theta$
• Twisted C-brackets
• Courant bracket found out to be T-dual to Roytenberg bracket
• Marginal deformations and quasi-Hopf algebras
• On the limitations of non-geometric fluxes to realize dS vacua
• Metastable vacua from torsion and machine learning
• Taxonomy of scalar potential with U-dual fluxes
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• T-folds as Poisson-Lie plurals
• Fluxes of Courant bracket twisted at the same time by $B$ and $\theta$
• On topology changes in quantum field theory and quantum gravity
• Open-String Non-Associativity in an R-flux Background
• Reductions of Exceptional Field Theories
• World-volume Effective Theories of Locally Non-geometric Branes
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Moduli spaces of non-geometric type II/heterotic dual pairs
• Interactions of strings on a T-fold
• Lagrangian formulation for electric charge in a magnetic monopole distribution
• Torus Bundles, Automorphisms and T-Duality
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras
• Instances of Higher Geometry in Field Theory
• Towards a String Realization of the Dark Dimension via T-folds
• Systematic exploration of the non-geometric flux landscape
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• A T-Fold Black Hole in Doubled Type IIB