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.

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

References in corpus (71)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Double Field Theory
• Flux Compactification
• Distance and de Sitter Conjectures on the Swampland
• Doubled Geometry and T-Folds
• Generalized Geometry and M theory
• Duality and Dilaton
• Exceptional Field Theory III: E${}_{8(8)}$
• On non-abelian T-dual geometries with Ramond fluxes
• Lectures on Gauged Supergravity and Flux Compactifications
• Inflationary Constraints on Type IIA String Theory
• Gauged Double Field Theory
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• T-duality and closed string non-commutative (doubled) geometry
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Lectures on Generalized Complex Geometry for Physicists
• Abelian Yang-Baxter Deformations and TsT transformations
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Spacetimes for λ-deformations
• Background Field Equations for the Duality Symmetric String
• Torsional Heterotic Geometries
• Charting the landscape of N=4 flux compactifications
• Frame-like Geometry of Double Field Theory
• D terms from D-branes, gauge invariance and moduli stabilization in flux compactifications
• Lectures on Nongeometric Flux Compactifications
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds
• Flux Compactifications of M-Theory on Twisted Tori
• T-duality for principal torus bundles
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• Toroidal Orientifolds in IIA with General NS-NS Fluxes
• Towards Axionic Starobinsky-like Inflation in String Theory
• The KK-Monopole/NS5-Brane in Doubled Geometry
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
• $T$-folds from Yang-Baxter deformations
• T-duality with H-flux: non-commutativity, T-folds and G x G structure
• Algebras and non-geometric flux vacua
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Non-geometric flux vacua, S-duality and algebraic geometry
• T-duality in Ramond-Ramond backgrounds
• NS-NS fluxes in Hitchin's generalized geometry
• Low Energy Supersymmetry from Non-Geometry
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• The N=1 Low-Energy Effective Action of Spontaneously Broken N=2 Supergravities
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• Marginal and non-commutative deformations via non-abelian T-duality
• Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry
• Type IIB flux vacua from G-theory II
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• A Lorentz invariant doubled worldsheet theory
• Type IIB flux vacua from G-theory I
• On general flux backgrounds with localized sources
• Effective descriptions of branes on non-geometric tori
• Canonical pure spinor (Fermionic) T-duality
• Semi-Flatland
• Mirrorfolds with K3 Fibrations
• Unwinding strings in semi-flatland
• On T-duality transformations for the three-sphere
• Non-Geometric F-Theory-Heterotic Duality
• Aspects of the Doubled Worldsheet
• States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution
• Locally non-geometric fluxes and missing momenta in M-theory
• Backreacted T-folds and non-geometric regions in configuration space
• Freed-Witten anomaly in general flux compactification
• Small magnetic charges and monopoles in non-associative quantum mechanics
• Partial SUSY Breaking for Asymmetric Gepner Models and Non-geometric Flux Vacua
• Poisson-Lie T-plurality as canonical transformation

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