Flux Compactification

Abstract

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.

66 pages, 3 figures, Latex with revtex4 macros. v3: version to appear in RMP

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• Open string wavefunctions in flux compactifications
• The Boundaries of KKLT
• Yang-Mills instantons and dyons on homogeneous G_2-manifolds
• Neutralino, axion and axino cold dark matter in minimal, hypercharged and gaugino AMSB
• Fluxes and Warping for Gauge Couplings in F-theory
• Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
• TASI lectures on complex structures
• Bouncing Universe from Nothing
• Induced vacuum currents in anti-de Sitter space with toral dimensions
• Field dynamics and tunneling in a flux landscape
• A landscape solution to the SUSY flavor and CP problems
• Inflation, String Theory and Cosmology
• Metastable Vacua in Perturbed Seiberg-Witten Theories, Part 2: Fayet-Iliopoulos Terms and Kähler Normal Coordinates
• Non-perturbative effective interactions from fluxes
• Two Notions of Naturalness
• On D-brane moduli stabilisation
• Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
• The Physical Process First Law for Bifurcate Killing Horizons
• Reducing democratic type II supergravity on SU(3) x SU(3) structures
• A special road to AdS vacua
• Slow-roll inflation in (R+R*4) gravity
• Double quiver gauge theory and nearly Kahler flux compactifications
• Putting the Boot into the Swampland
• On the superstring-inspired quantum correction to the Starobinsky model of inflation
• Desensitizing Inflation from the Planck Scale
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Probing the Geometry of Warped String Compactifications at the LHC
• Yukawa hierarchies at the point of $E_8$ in F-theory
• Gaugino Anomaly Mediated SUSY Breaking: phenomenology and prospects for the LHC
• Relating Double Field Theory to the Scalar Potential of N=2 Gauged Supergravity
• Moduli Stabilization in Meta-Stable Heterotic Supergravity Vacua
• Induced fermionic current densities by magnetic flux in higher dimensional cosmic string spacetime
• Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape
• Runaway dilatonic domain walls
• Type IIB flux vacua from G-theory II
• Systematics of Type IIA moduli stabilisation
• Heavy quarks in the presence of higher derivative corrections from AdS/CFT
• Accidental Inflation in the Landscape
• Tensors, non-Gaussianities, and the future of potential reconstruction
• On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
• Scanning the Landscape of Flux Compactifications: Vacuum Structure and Soft Supersymmetry Breaking
• Effective field theory for magnetic compactifications
• Fermionic vacuum polarization by a composite topological defect in higher-dimensional space-time
• Towards Matter Inflation in Heterotic String Theory
• Local String Models and Moduli Stabilisation
• Future Foam
• N=1 Sigma Models in AdS_4
• Inflating an Inhomogeneous Universe
• Fast optimization algorithms and the cosmological constant
• DBI N-flation
• New solutions with accelerated expansion in string theory
• On Metastable Branes and a New Type of Magnetic Monopole
• The scale of gravity and the cosmological constant within a landscape
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Oxidised cosmic acceleration
• On de Sitter Spacetime and String Theory
• Physical Vacua in IIB Compactifications with a Single Kaehler Modulus
• On general flux backgrounds with localized sources
• The Higgs field and early universe cosmology: a (brief) review
• Kahler Independence of the G2-MSSM
• Non-geometric fluxes as supergravity backgrounds
• Index Theorems on Torsional Geometries
• Heterotic compactifications on SU(2)-structure backgrounds
• Scalar potential in F(R) supergravity
• Relaxing Isocurvature Bounds on String Axion Dark Matter
• General Relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum
• A Stringy Mechanism for A Small Cosmological Constant
• A Stringy Mechanism for A Small Cosmological Constant - Multi-Moduli Cases -
• Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization
• String Cosmology - Large-Field Inflation in String Theory
• Decay of flux vacua to nothing
• Type IIA Flux Vacua with Mobile D6-branes
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• No-scale supersymmetry breaking vacua and soft terms with torsion
• Gravity waves and the LHC: Towards high-scale inflation with low-energy SUSY
• De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications
• Orientifold Calabi-Yau Threefolds with Divisor Involutions and String Landscape
• Cascading to the MSSM
• Stretched extra dimensions and bubbles of nothing in a toy model landscape
• An obstacle to populating the string theory landscape
• Quark and Lepton Masses from Gaussian Landscapes
• Exceptional N=6 and N=2 AdS_4 Supergravity, and Zero-Center Modules
• Revealing systematics in phenomenologically viable flux vacua with reinforcement learning
• Vacuum currents in braneworlds on AdS bulk with compact dimensions
• The Euler characteristic correction to the Kaehler potential - revisited
• Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-branes geometry
• Fibre Inflation and Reheating
• Disorder on the landscape
• Probability of Slowroll Inflation in the Multiverse
• Inflation on an Open Racetrack
• Inflation with large supergravity corrections
• Dictionary for the type II nongeometric flux compactifications
• Gribov ambiguity in asymptotically AdS three-dimensional gravity
• Introductory Lectures on Extended Supergravities and Gaugings
• Axions as Hot and Cold Dark Matter
• RG-Induced Modulus Stabilization: Perturbative de Sitter Vacua and Improved $D3$-$\overline{D3}$ Inflation
• Chain inflation revisited
• Learning non-Higgsable gauge groups in 4D F-theory
• A Parallel World in the Dark
• Resonant Tunneling in Superfluid Helium-3
• Building a Nest at Tree Level: Classical Metastability and Non-Trivial Vacuum Structure in Supersymmetric Field Theories
• D(-1)-Instanton Superpotential In String Theory
• Dark Energy and String Theory
• Moduli Stabilisation and the Statistics of SUSY Breaking in the Landscape
• Distribution of the Number of Generations in Flux Compactifications
• Universal Axion Backreaction in Flux Compactifications
• Contact Manifolds, Contact Instantons, and Twistor Geometry
• N-ification of Forces: A Holographic Perspective on D-brane Model Building
• Runaway in the Landscape
• Statistics of Flux Vacua for Particle Physics
• A Gravitino-rich Universe
• Tuned and Non-Higgsable U(1)s in F-theory
• Phenomenology of Infrared Smooth Warped Extra Dimensions
• Correlation Classes on the Landscape: To What Extent is String Theory Predictive?
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• N=2 Moduli of AdS4 vacua: A fine-print study
• The Equivalence Principle and the Constants of Nature
• Gaugino mass term for D-branes and Generalized Complex Geometry
• Rigid nongeometric orientifolds and the swampland
• Affleck-Dine Baryogenesis in Effective Supergravity
• Casimir effect for scalar current densities in topologically nontrivial spaces
• The Scale of Inflation in the Landscape
• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Massive quiver matrix models for massive charged particles in AdS
• Dirac structures on nilmanifolds and coexistence of fluxes
• M-Theory and Maximally Supersymmetric Gauge Theories
• Inflation Expels Runaways
• Spin(7)-manifolds in compactifications to four dimensions
• Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds
• Polarized light-by-light scattering at the CLIC induced by axion-like particles
• Cosmological Bounds on sub-GeV Dark Vector Bosons from Electromagnetic Energy Injection
• Topological Eternal Hilltop Inflation and the Swampland Criteria
• Pseudo-redundant vacuum energy
• Axion Landscape Cosmology
• BPS and non BPS 7D Black Attractors in M-Theory on K3
• Twisting K3 x T^2 Orbifolds
• Tunneling and propagation of vacuum bubbles on dynamical backgrounds
• Continuous degeneracy of non-supersymmetric vacua
• Cosmological dynamics of multifield dark energy
• TeV-Scale strings
• Gaugings at angles from orientifold reductions
• The Degeneracy Problem in Non-Canonical Inflation
• Persistent Homology and String Vacua
• On the superstrings-induced four-dimensional gravity, and its applications to cosmology
• Effect of reheating on predictions following multiple-field inflation
• Induced fermionic currents in de Sitter spacetime in the presence of a compactified cosmic string
• A symplectic rearrangement of the four dimensional non-geometric scalar potential
• Reading off the non-geometric scalar potentials via topological data of the Calabi Yau manifolds
• Compactifying de Sitter Naturally Selects a Small Cosmological Constant
• Exploring ALPs beyond the canonical
• Freedom and Constraints in the K3 Landscape
• Brane Inflation and the Overshoot Problem
• The Spectra of Type IIB Flux Compactifications at Large Complex Structure
• New model of axion monodromy inflation and its cosmological implications
• Cosmology from String Theory
• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Higher derivative corrections to the entropic force from holography
• Fitting fermion masses and mixings in F-theory GUTs
• Runaway Domain Wall and Space-time Varying alpha
• Accidental Inflation from Kähler Uplifting
• Weak Gravity Conjecture for the Effective Field Theories with N Species
• Systematics of perturbatively flat flux vacua
• Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory
• Revisiting toric SU(3) structures
• Classical de Sitter solutions in three dimensions without tachyons?
• Rigid Limit in N=2 Supergravity and Weak-Gravity Conjecture
• Towards a complete mass spectrum of type-IIB flux vacua at large complex structure
• Low energy supersymmetry from R-symmetries
• String Theory, the Dark Sector and the Hierarchy Problem
• A Smooth Landscape: Ending Saddle Point Inflation Requires Features to be Shallow
• Axionic Band Structure of the Cosmological Constant
• Time warps
• Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory
• Holographic Perspectives On Models Of Moduli Stabilization In M-Theory
• Low energy effective theory on a regularized brane in six-dimensional flux compactifications
• Phase transitions of black strings in dynamical Chern-Simons modified gravity
• Kaluza-Klein theory in the limit of large number of extra dimensions
• Dark Matter and Naturalness
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Combining High-scale Inflation with Low-energy SUSY
• Flux-induced Soft Terms on Type IIB/F-theory Matter Curves and Hypercharge Dependent Scalar Masses
• Neutrino mixing and mass hierarchy in Gaussian landscapes
• On Gauge Mediated SUSY Breaking and Moduli Stabilization
• Flux Vacua and Modularity for ${\mathbb{Z}}_2$ Symmetric Calabi-Yau Manifolds
• Type IIA orientifold compactification on SU(2)-structure manifolds
• Radiative natural supersymmetry emergent from the string landscape
• Order ${\alpha }^{\prime }$ heterotic domain walls with warped nearly Kähler geometry
• Inflaxion Dark Matter
• Standard Model from A Supergravity Model with a Naturally Small Cosmological Constant
• Kähler moduli inflation and WMAP7
• Measures for a Transdimensional Multiverse
• de Sitter vacua from an anomalous gauge symmetry
• KKLT without AdS
• Stringy Bubbles Solve de Sitter Troubles
• Bound on largest $r\lesssim 0.1$ from sub-Planckian excursions of inflaton
• Holographic de Sitter Universe
• On stable type IIA de-Sitter vacua with geometric flux
• Type IIB Flux Vacua from M-theory via F-theory
• Observational Constraints on Axions as Quintessence in String Theory
• Phase transitions during Cyclic-Inflation and Non-gaussianity
• Analytics of type IIB flux vacua and their mass spectra
• Stabilizing massless fields with fluxes in Landau-Ginzburg models
• Dark matter and dark radiation from the early universe with a modulus coupled to the PQMSSM
• Non-supersymmetric branes
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Why do we observe a weak force? The hierarchy problem in the multiverse
• A Landscape of AdS Flux Vacua
• Instantons on sine-cones over Sasakian manifolds
• Restrictions on infinite sequences of type IIB vacua
• Shift-symmetries and gauge coupling functions in orientifolds and F-theory
• Flux Attractors and Generating Functions
• Particle Production during Inflation in Light of PLANCK
• Flux Compactifications on $(S_2{)}^N$
• Compact objects and the swampland
• Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure
• Inflation in Random Landscapes with two energy scales
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Landscape Higgs and sparticle mass predictions from a logarithmic soft term distribution
• On NS5-brane instantons and volume stabilization
• The shadow of dark matter as a shadow of string theory
• Axion Stabilization in Type IIB Flux Compactifications
• A new class of de Sitter vacua in String Theory Compactifications
• Moduli Stabilisation in Heterotic Models with Standard Embedding
• Remark on Calabi-Yau vacua of the string theory and the cosmological constant problem
• Fine-tuned vs. natural supersymmetry: what does the string landscape predict?
• Minimal Starobinsky supergravity coupled to dilaton-axion superfield
• Matching WMAP 3-yrs results with the Cosmological Slingshot Primordial Spectrum
• Perturbations in Bouncing and Cyclic Models, a General Study
• Warming up the Fibres
• Tensor modes on the string theory landscape
• Emergent Dark Energy from Dark Matter
• Strongly Coupled Inflaton
• GUTs without guts
• Kahler Moduli Inflation in Type IIB Compactifications: A random tumble through the Calabi-Yau landscape
• A counterexample to the Nelson-Seiberg theorem
• A Simple System For Coleman-De Luccia Transitions
• Distribution of supersymmetry mu parameter and Peccei-Quinn scale f_a from the landscape
• Applications of an exact counting formula in the Bousso-Polchinski Landscape
• Generating functions for intersection products of divisors in resolved F-theory models
• Orientiholes
• Axionlike Origin of the Primordial Density Perturbation
• Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime
• $R^2$ corrections to holographic Schwinger effect
• Lessons from the Vacuum Structure of 4d N=2 Supergravity
• Family Unification via Quasi-Nambu-Goldstone Fermions in String Theory
• Mass spectrum in a six-dimensional $SU(n)$ gauge theory on a magnetized torus
• When effective theories predict: the inevitability of Mercury's anomalous perihelion precession
• Gravity waves from cosmic bubble collisions
• Vacuum polarization by fermionic fields in higher dimensional cosmic string space-time
• A Toy Model for Gauge-Mediation in Intersecting Brane Models
• Heterotic T-folds with a small number of neutral moduli
• Can Compactifications Solve the Cosmological Constant Problem?
• Left-invariant Einstein metrics on $S^3\times S^3$
• A Cosmological Constant That is Too Small
• Compact objects with scalar charge embedded in a magnetic or electric field in Einstein-Maxwell-dilaton theories
• Dynamics of Matter in a Compactified Kaluza-Klein Model
• A sufficient condition for counterexamples to the Nelson-Seiberg theorem
• Fate of homogeneous ${\mathbb{Z}}_2$-symmetric scalar condensates
• Reheating and Entropy Perturbations in Fibre Inflation
• Quantum Cosmology in Four Dimensions
• Computation Of Some Zamolodchikov Volumes, With An Application
• Linking the Supersymmetric Standard Model to the Cosmological Constant
• On Stringy de Sitter Spacetimes
• Moduli Evolution in the Presence of Matter Fields and Flux Compactification
• Exploring a simple sector of the Einstein-Maxwell landscape
• BPS jumping loci are automorphic
• Probing Particle Physics with Gravitational Waves
• SL(2,R) covariant conditions for N=1 flux vacua
• Sub-MeV Bosonic Dark Matter, Misalignment Mechanism and Galactic Dark Matter Halo Luminosities
• Coisotropic D-branes on AdS4 x CP3 and massive deformations
• Statistics of Stationary Points of Random Finite Polynomial Potentials
• Moduli Backreaction on Inflationary Attractors
• On four-derivative terms in IIB Calabi-Yau orientifold reductions
• BPS-like potential for compactifications of heterotic M-theory?
• Can QCD Axion Stars explain Subaru HSC microlensing?
• Impact of Helical Electromagnetic Fields on the Axion Window
• Phenomenology from the Landscape of String Vacua
• Taxonomy of scalar potential with U-dual fluxes
• Enhancement of axion decay constants in type IIA theory?
• Axion-like particle dark matter in the linear regime of structure formation
• Higgs in Nilpotent Supergravity: Vacuum Energy and Festina Lente
• $R^4$ corrections to holographic Schwinger effect
• High Energy Physics and Cosmology at the Unification Frontier: Opportunities and Challenges in the coming years
• Gauged Supergravities and the Physics of Extra Dimensions
• Cosmic Microwave Background Dipole Asymmetry could be explained by Axion Monodromy Cosmic Strings
• Dark Matter density and the Higgs mass in LVS String Phenomenology
• Off-shell $N=2\to N=1$ reduction in 4D conformal supergravity
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• Numerically Investigating the Emergent Cyclic Inflation Scenario
• The Higgs mass and the scale of SUSY breaking in the NMSSM
• Vacuum statistics and parameter tuning for F-term supersymmetry breaking
• The Large Number Limit of Multifield Inflation
• A Stronger Case for Superunification Post Higgs Boson Discovery
• Time dependent action in ${\varphi }^6$ potential
• Mediation of Supersymmetry Breaking in a Class of String Theory Models
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• Flux Compactifications Grow Lumps
• Extended Metastable Dark Energy
• Landscape versus Swampland for Higher Derivative Gravity
• On special geometry of the moduli space of string vacua with fluxes
• Type IIA Flux Vacua and ${\alpha }^{\prime }$-corrections
• Electric Field Decay Without Pair Production: Lattice, Bosonization and Novel Worldline Instantons
• A formal notion of genericity and term-by-term vanishing superpotentials at supersymmetric vacua from R-symmetric Wess-Zumino models
• Electronic structure and exotic exchange splitting in spin-density-wave states of BaFe${}_2$As${}_2$
• Fluxes, Twisted tori, Monodromy and $U(1)$ Supermembranes
• Non-minimally coupled multi-scalar black holes
• Status of Superstring and M-Theory
• Probability of Vacuum Stability in Type IIB Multi-Kähler Moduli Models
• A worldsheet perspective on string inflation
• On the boundedness of effective potentials arising from string compactifications
• Brane world regularization of point particle classical self-energy
• Type IIA/M-theory Moduli fixing in a Class of Orientifold Models
• Sparticle and Higgs boson masses from the landscape: dynamical versus spontaneous supersymmetry breaking
• Strings and D-branes in a supersymmetric magnetic flux background
• Nonlinear dynamics of flux compactification
• Black branes in flux compactifications
• Novel counterexample to the Nelson-Seiberg theorem
• 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
• Higher rank antisymmetric tensor fields in Klebanov-Strassler geometry
• De Sitter space constraints on brane tensions and couplings
• Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with $G_2$-structure
• Generalised Geometry and Flux Vacua
• Nonexistence of supersymmetry breaking counterexamples to the Nelson-Seiberg theorem
• Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds
• Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms
• Our Place in a Vast Universe
• Supersymmetric Inflation from the Fifth Dimension
• Choices of spinor inner products on M-theory backgrounds
• Quark Masses: An Environmental Impact Statement
• Hypermoduli Stabilization, Flux Attractors, and Generating Functions
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras
• Generalized Geometry and Partial Supersymmetry Breaking
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization
• Moduli Stabilisation on the Worldsheet
• A new mechanism for freezing extra dimensions with higher-order curvature terms
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Flux Backgrounds and Exceptional Generalised Geometry
• Dimensional Reductions of DFT and Mirror Symmetry for Calabi-Yau Three-folds and $K3\times T^2$
• Topics in vacuum decay (Ph.D Thesis)
• Bounds on complex structure moduli values for perturbative control
• Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
• Supersymmetric Horizons at the Edge of Effective Field Theory
• Curvature perturbations from vacuum transition during inflation
• Measures in Mutlifield Inflation
• Preferred hierarchy scales from the product landscape
• Modeling M-Theory Vacua via Gauged S-Duality
• Remarks on positive energy vacua via effective potentials in string theory
• Gauge Symmetry Restoration by Higgs Condensation in Flux Compactifications on Coset Spaces
• Soft supersymmetry breaking with tiny cosmological constant in flux compactified N=1 Supergravity
• Avoiding recollapse in an open-AdS universe via a self-tuning-like mechanism
• Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity
• A T-Fold Black Hole in Doubled Type IIB
• Systematic exploration of the non-geometric flux landscape
• Moduli Stabilization in Stringy ISS Models
• Topics in Supergravity Phenomenology
• Starobinsky-Bel-Robinson gravity
• Life on moduli space?
• Probing the Structure of String Theory Vacua with Genetic Algorithms and Reinforcement Learning
• Light and compressed gluinos at the LHC via string theory
• Breathing Vacuum Bubbles in Five-Dimensional Gauss-Bonnet Gravity
• Aspects of moduli stabilization in type IIB string theory
• DWSB for heterotic flux compactifications
• Warped spherical compactifications in the gravity theory
• Minkowski vacuum transitions in (non-geometric) flux compactifications
• Unimodular time in JT gravity: a holographic clock
• A Perfectoid Duality Between M-Theory and F-Theory
• Non-Gaussianity after many-field reheating