Flux compactifications in string theory: a comprehensive review

Abstract

We present a pedagogical overview of flux compactifications in string theory, from the basic ideas to the most recent developments. We concentrate on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyze the resulting four-dimensional effective theories, as well as some of its perturbative and non-perturbative corrections, focusing on moduli stabilization. Finally, we briefly review statistical studies of flux backgrounds.

85 pages, 2 figures. v2, v3: minor changes, references added

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• N=1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes
• A Heterotic Standard Model
• Distributions of nonsupersymmetric flux vacua
• Supersymmetric Standard Model Spectra from RCFT orientifolds
• Supersymmetric AdS(4) compactifications of IIA supergravity
• Flux-induced SUSY-breaking soft terms on D7-D3 brane systems
• Flux-induced Soft Supersymmetry Breaking in Chiral Type IIB Orientifolds with D3/D7-Branes
• Building MSSM Flux Vacua
• The Baryonic Branch of Klebanov-Strassler Solution: a Supersymmetric Family of SU(3) Structure Backgrounds
• Stringy corrections to Kahler potentials, SUSY breaking, and the cosmological constant problem
• The Statistics of Supersymmetric D-brane Models
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• MSSM vacua from Flux Compactifications
• Heterotic on Half-flat
• Basic results in Vacuum Statistics
• On the Explicit Construction and Statistics of Calabi-Yau Flux Vacua
• General N = 1 Supersymmetric Fluxes in Massive Type IIA String Theory
• Chiral D-brane Models with Frozen Open String Moduli
• The spinorial geometry of supersymmetric backgrounds
• Effective action of (massive) IIA on manifolds with SU(3) structure
• Statistics of M theory Vacua
• Moduli Potentials in Type IIA Compactifications with RR and NS Flux
• Generalised $G_2$-structures and type IIB superstrings
• Gauged supergravity algebras from twisted tori compactifications with fluxes
• D3 Brane Action and Fermion Zero Modes in Presence of Background Flux
• Gauging the Heisenberg algebra of special quaternionic manifolds
• Branes on Generalized Calibrated Submanifolds
• Standard-like Models as Type IIB Flux Vacua
• Topological mirror symmetry with fluxes
• Counting fermionic zero modes on M5 with fluxes
• N=2 Supergravity Lagrangian Coupled to Tensor Multiplets with Electric and Magnetic Fluxes
• The Scherk-Schwarz mechanism as a flux compactification with internal torsion
• Topological constraints on stabilized flux vacua
• Generalized complex geometry, generalized branes and the Hitchin sigma model
• M-theory Compactifications on Manifolds with G2 Structure
• Type II Strings and Generalized Calabi-Yau Manifolds
• Systematics of M-theory spinorial geometry
• A sigma model field theoretic realization of Hitchin's generalized complex geometry
• Supersymmetric Standard Models, Flux Compactification and Moduli Stabilization
• Volume Stabilization via ${\alpha }^{\prime }$ Corrections in Type IIB Theory with Fluxes
• General Type IIB Fluxes with SU(3) Structures
• Refining G-structure classifications
• Superstring Orientifolds with Torsion: O5 Orientifolds of Torus Fibrations and their Massless Spectra
• Flux Vacua Statistics for Two-Parameter Calabi-Yau's
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• Instantons on sine-cones over Sasakian manifolds
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• Supersymmetric branes on curved spaces and fluxes
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
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• Massless fermionic bound states and the gauge/gravity correspondence
• Axion Stabilization in Type IIB Flux Compactifications
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• A Heterotic Flux Background and Calibrated Five-Branes
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• AdS Vacua, Attractor Mechanism and Generalized Geometries
• Testing the gaugino AMSB model at the Tevatron via slepton pair production
• Discretized Gravity in 6D Warped Space
• Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives
• M-theory Compactifications to Three Dimensions with M2-brane Potentials
• Effective field theory analysis of the self-interacting chameleon
• Special Lagrangian cycles and Calabi-Yau transitions
• Purely non-perturbative AdS vacua and the swampland
• Deep learning complete intersection Calabi-Yau manifolds
• The Super-Stuckelberg procedure and dS in Pure Supergravity
• A counterexample to the Nelson-Seiberg theorem
• Generalized CoKähler Geometry and an Application to Generalized Kähler Structures
• Black Holes and Fourfolds
• A doubly covariant formula of deficit angle and its application to six-dimensional braneworld
• Invariant Killing spinors in 11D and type II supergravities
• The Lie algebroid Poisson sigma model
• Couplings of N=1 chiral spinor multiplets
• Topological A-Type Models with Flux
• Left-invariant Einstein metrics on $S^3\times S^3$
• A Toy Model for Gauge-Mediation in Intersecting Brane Models
• Hybrid Formalism, Supersymmetry Reduction, and Ramond-Ramond Fluxes
• Moduli identification methods in Type II compactifications
• A method of deforming G-structures
• Heterotic T-folds with a small number of neutral moduli
• Gravity with antisymmetric components
• Interpolation of partial and full supersymmetry breakings in $\mathcal{N}=2$ supergravity
• M-theory on non-Kähler manifolds
• Mass spectrum in a six-dimensional $SU(n)$ gauge theory on a magnetized torus
• A sufficient condition for counterexamples to the Nelson-Seiberg theorem
• Instantons on Calabi-Yau cones
• Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds
• Superspaces for heterotic pure spinor string compactifications
• Type IIB Flows with N=1 Supersymmetry
• Lie algebroids, non-associative structures and non-geometric fluxes
• Courant bracket twisted both by a 2-form $B$ and by a bi-vector $\theta$
• On four-derivative terms in IIB Calabi-Yau orientifold reductions
• Coisotropic D-branes on AdS4 x CP3 and massive deformations
• On Susy Standard-like models from orbifolds of D=6 Gepner orientifolds
• Moduli Backreaction on Inflationary Attractors
• Off-shell $N=2\to N=1$ reduction in 4D conformal supergravity
• New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations
• $G_2$ holonomy metrics and wrapped D6-branes
• Invariant Generalized Complex Structures on Partial Flag Manifolds
• Taxonomy of scalar potential with U-dual fluxes
• Instantons on conical half-flat 6-manifolds
• BPS-like potential for compactifications of heterotic M-theory?
• Deforming D-brane models on $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_{2M})$ orbifolds
• Dark Matter density and the Higgs mass in LVS String Phenomenology
• Non-perturbative scalar potential inspired by type IIA strings on rigid CY
• G2-structures for N=1 supersymmetric AdS4 solutions of M-theory
• A class of non-supersymmetric orientifolds
• The Large Number Limit of Multifield Inflation
• Spinors of real type as polyforms and the generalized Killing equation
• Mediation of Supersymmetry Breaking in a Class of String Theory Models
• Smarr's Formula in Eleven-Dimensional Supergravity
• Generalised holonomies and K(E${}_9$)
• Electronic structure and exotic exchange splitting in spin-density-wave states of BaFe${}_2$As${}_2$
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• Meromorphic Flux Compactification
• From Twists and Shifts to L-R asymmetric D-branes
• A formal notion of genericity and term-by-term vanishing superpotentials at supersymmetric vacua from R-symmetric Wess-Zumino models
• Vacuum statistics and parameter tuning for F-term supersymmetry breaking
• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Invariant generalized complex geometry on maximal flag manifolds and their moduli
• Phenomenology of Strong Interactions -- Towards an Effective Theory for Low Energy QCD
• Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds
• Finite Temperature Behaviour of O'KKLT Model
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• On the role of torsion and higher forms in off-shell supergravity
• Novel counterexample to the Nelson-Seiberg theorem
• Half-flat Quantum Hair
• A General Study of Ground States of N=2 Supergravity Theories with Symmetric Scalar Manifolds in 5 Dimensions
• Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms
• Brane world regularization of point particle classical self-energy
• Type IIA/M-theory Moduli fixing in a Class of Orientifold Models
• "Big" Divisor D3/D7 Swiss Cheese Phenomenology
• Generalised Geometry and Flux Vacua
• Choices of spinor inner products on M-theory backgrounds
• Compactification of IIB Theory with Fluxes and Axion-Dilaton String Cosmology
• The Generalised Geometry of Type II Non-Geometric Fluxes Under T and S Dualities
• Black branes in flux compactifications
• Late-time Cosmology without Dark Sector but with Closed String Massless Sector
• Nonexistence of supersymmetry breaking counterexamples to the Nelson-Seiberg theorem
• Supergravity Fluxes and Generalised Geometry
• Behaviors of two supersymmetry breaking scales in $\mathcal{N}=2$ supergravity
• Spherically symmetric solution in a space-time with torsion
• Dimensional Reductions of DFT and Mirror Symmetry for Calabi-Yau Three-folds and $K3\times T^2$
• Classification of Modular Symmetries in Type IIB Flux Landscape
• Generalized Geometry and Partial Supersymmetry Breaking
• Remarks on positive energy vacua via effective potentials in string theory
• Near-Horizon geometry from flux compactification
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Preferred hierarchy scales from the product landscape
• Modeling M-Theory Vacua via Gauged S-Duality
• Hypermoduli Stabilization, Flux Attractors, and Generating Functions
• A companion to "Knot invariants and M-theory I'' [arXiv:1608.05128]: proofs and derivations
• One-loop effective action in $\mathcal{N}=2$ supersymmetric massive Yang-Mills theory
• Smooth tensionful higher-codimensional brane worlds with bulk and brane form fields
• Slow-roll Analysis of Double Field Axion Inflation
• Heterotic Strings on Generalized Calabi-Yau Manifolds and Kaehler Moduli Stabilization
• On Issues in Swiss Cheese Compactifications
• Gauge field fluxes and Bianchi identities in extended field theories
• Orientifolding in N=2 Superspace
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras
• Supersymmetric Horizons at the Edge of Effective Field Theory
• Flux-induced isometry gauging in heterotic strings
• Gauge Symmetry Restoration by Higgs Condensation in Flux Compactifications on Coset Spaces
• Bounds on complex structure moduli values for perturbative control
• Marginally deformed AdS${}_5$/CFT${}_4$ Backgrounds in Type IIB
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Cylinder quantum field theories at small coupling
• Non-Gaussianity after many-field reheating
• Avoiding recollapse in an open-AdS universe via a self-tuning-like mechanism
• A T-Fold Black Hole in Doubled Type IIB
• Machine Learning Calabi-Yau Three-Folds, Four-Folds, and Five-Folds
• A Massive S-duality in 4 dimensions
• Minkowski vacuum transitions in (non-geometric) flux compactifications
• No inflation in type IIA strings on rigid CY spaces
• Testing Gaugino Mass Unification Directly at the LHC
• DWSB for heterotic flux compactifications
• A heterotic sigma model with novel target geometry
• Invariant generalized almost complex structures on real flag manifolds
• Non-unimodular reductions and N = 4 gauged supergravities
• Systematic exploration of the non-geometric flux landscape
• Nearly-Kaehler dimensional reduction of the heterotic string
• $\epsilon$-contact structures and six-dimensional supergravity