Les Houches Lectures on Constructing String Vacua

Abstract

These lectures give a detailed introduction to constructing and analyzing string vacua suitable for phenomenological model building, with particular emphasis on F-theory flux vacua. Topics include (1) general challenges and overview of some proposed scenarios, (2) an extensive introduction to F-theory and its relation to M-theory and perturbative IIB string theory, (3) F-theory flux vacua and moduli stabilization scenarios, (4) a practical geometrical toolkit for constructing string vacua from scratch, (5) statistics of flux vacua, and (6) explicit models.

127 pages, 17 figures

References in corpus (71)

• A Large Mass Hierarchy from a Small Extra Dimension
• de Sitter Vacua in String Theory
• Hierarchies from Fluxes in String Compactifications
• Phases of $N=2$ Theories In Two Dimensions
• Eleven-Dimensional Supergravity on a Manifold with Boundary
• Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
• Towards Inflation in String Theory
• Supergravity description of field theories on curved manifolds and a no go theorem
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• M Theory, Orientifolds and G-Flux
• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• Fivebranes, Membranes and Non-Perturbative String Theory
• The statistics of string/M theory vacua
• Non-Perturbative Superpotentials In String Theory
• The Anthropic Landscape of String Theory
• Geometric Singularities and Enhanced Gauge Symmetries
• Distributions of flux vacua
• M-Theory on Eight-Manifolds
• Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials
• On Flux Quantization In M-Theory And The Effective Action
• Eleven Dimensional Origin of String/String Duality: A One Loop Test
• Moduli Stabilization from Fluxes in a Simple IIB Orientifold
• New Vacua for Type II String Theory
• The effective action of N=1 Calabi-Yau orientifolds
• Building a Better Racetrack
• Type IIA Moduli Stabilization
• Inflation and Eternal Inflation
• Scales and hierarchies in warped compactifications and brane worlds
• On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes
• Calabi-Yau fourfolds for M- and F-Theory compactifications
• Distributions of nonsupersymmetric flux vacua
• Dynamics of warped compactifications and the shape of the warped landscape
• Gauge Dynamics And Compactification To Three Dimensions
• Soft Supersymmetry Breaking in Calabi-Yau Orientifolds with D-branes and Fluxes
• String Theory on Calabi-Yau Manifolds
• Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
• Orientifold Limit of F-theory Vacua
• A Delicate Universe
• Progress in D-brane model building
• Simple de Sitter Solutions
• Model Building with F-Theory
• M-theory compactified on Calabi-Yau fourfolds with background flux
• Flux Compactifications on Calabi-Yau Threefolds
• Superpotentials and Membrane Instantons
• Computational complexity of the landscape I
• Enumerating Flux Vacua with Enhanced Symmetries
• Moduli Stabilization in Type IIB Orientifolds (II)
• Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications
• Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons
• An Open String Landscape
• A Moduli Fixing Mechanism in M theory
• Holographic Action for the Self-Dual Field
• Moduli Stabilization in Type IIB Orientifolds (I)
• Moduli Stabilization in Non-Geometric Backgrounds
• N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
• Branches of the Landscape
• New string vacua from twistor spaces
• D7-Brane Motion from M-Theory Cycles and Obstructions in the Weak Coupling Limit
• The Ubiquitous Throat
• Warping and Supersymmetry Breaking
• Topological constraints on stabilized flux vacua
• Massive IIA flux compactifications and U-dualities
• Lectures on instantons
• Charting the landscape of supercritical string theory
• Stabilizing Moduli with a Positive Cosmological Constant in Heterotic M-Theory
• A Finite Landscape?
• Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory, I
• Fivebrane instantons and Calabi-Yau fourfolds with flux
• Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics
• New no-go theorems for cosmic acceleration with extra dimensions

Cited by in corpus (166)

• D-brane Instantons in Type II String Theory
• Tensionless Strings and the Weak Gravity Conjecture
• Lectures on F-theory compactifications and model building
• Global F-theory GUTs
• Landscape of superconducting membranes
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Classifying bases for 6D F-theory models
• Global aspects of the space of 6D N = 1 supergravities
• Matter and singularities
• D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation
• G_4 flux, chiral matter and singularity resolution in F-theory compactifications
• The dS swampland conjecture and the Higgs potential
• G-flux in F-theory and algebraic cycles
• Anomaly Equations and Intersection Theory
• Models of Particle Physics from Type IIB String Theory and F-theory: A Review
• AdS_6 solutions of type II supergravity
• Micromanaging de Sitter holography
• Toric bases for 6D F-theory models
• Cohomology of Line Bundles: A Computational Algorithm
• Physics of F-theory compactifications without section
• Magnetized E3-brane instantons in F-theory
• Asymptotic Flux Compactifications and the Swampland
• Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds
• Life at the Interface of Particle Physics and String Theory
• The Tadpole Problem
• Yukawa Couplings in F-theory and Non-Commutative Geometry
• Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
• A comment on effective field theories of flux vacua
• Tuning and Backreaction in F-term Axion Monodromy Inflation
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• The D5-brane effective action and superpotential in N=1 compactifications
• New F-theory lifts II: Permutation orientifolds and enhanced singularities
• Bounds on Slow Roll at the Boundary of the Landscape
• More on Dimension-4 Proton Decay Problem in F-theory -- Spectral Surface, Discriminant Locus and Monodromy
• A Stringy Origin of M2 Brane Chern-Simons Theories
• F-theory at order ${\alpha }^{\prime 3}$
• D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
• Minkowski 3-forms, Flux String Vacua, Axion Stability and Naturalness
• Matter wave functions and Yukawa couplings in F-theory Grand Unification
• dS Vacua and the Swampland
• On α' corrections in N=1 F-theory compactifications
• New Orientifold Weak Coupling Limits in F-theory
• Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses
• Heterotic Z6-II MSSM Orbifolds in Blowup
• On Cosmological Constants from alpha'-Corrections
• Scanning the skeleton of the 4D F-theory landscape
• F-theory flux vacua at large complex structure
• Warping the Kähler potential of F-theory/IIB flux compactifications
• Calabi-Yau threefolds with large h^{2, 1}
• ${\mathbb{P}}^1$-bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
• The N=1 effective actions of D-branes in Type IIA and IIB orientifolds
• Three-forms in Supergravity and Flux Compactifications
• Axion Inflation in F-theory
• Geometric constraints in dual F-theory and heterotic string compactifications
• Exploring The Holographic Swampland
• The anomaly that was not meant IIB
• The LVS Parametric Tadpole Constraint
• Five-Brane Superpotentials and Heterotic/F-theory Duality
• Anomaly Cancelation in Field Theory and F-theory on a Circle
• Moduli Stabilization in Asymptotic Flux Compactifications
• Special Points of Inflation in Flux Compactifications
• Quantum Gravity Constraints on Inflation
• Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds
• Hyperbolic compactification of M-theory and de Sitter quantum gravity
• A Note on Local GUT Models in F-Theory
• The Geometry of D-Brane Superpotentials
• Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Note on moduli stabilization, supersymmetry breaking and axiverse
• $P$ fluxes and exotic branes
• Open string wavefunctions in flux compactifications
• Gauge Coupling Unification in E6 F-Theory GUTs with Matter and Bulk Exotics from Flux Breaking
• Wavefunctions and the Point of E8 in F-theory
• CosmoBit: A GAMBIT module for computing cosmological observables and likelihoods
• TASI lectures on complex structures
• Fluxes and Warping for Gauge Couplings in F-theory
• Quantum Critical Dynamics from Black Holes
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Anomaly Inflow Methods for SCFT Constructions in Type IIB
• Desensitizing Inflation from the Planck Scale
• T-folds, doubled geometry, and the SU(2) WZW model
• Large Field Ranges from Aligned and Misaligned Winding
• Toric Methods in F-theory Model Building
• Tate Form and Weak Coupling Limits in F-theory
• Flux compactification on smooth, compact three-dimensional toric varieties
• New solutions with accelerated expansion in string theory
• Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds
• Gravity waves and the LHC: Towards high-scale inflation with low-energy SUSY
• CFTs Blueshift Tensor Fluctuations Universally
• Orientifold Calabi-Yau Threefolds with Divisor Involutions and String Landscape
• Les Houches lectures on inflationary observables and string theory
• The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
• Small flux superpotential in F-theory compactifications
• M/F-Theory as Mf-Theory
• On the Flux Vacua in F-theory Compactifications
• Tuned and Non-Higgsable U(1)s in F-theory
• Universal Axion Backreaction in Flux Compactifications
• Statistics of Flux Vacua for Particle Physics
• Compact T-branes
• Abelian Gauge Fluxes and Local Models in F-Theory
• The Scale of Inflation in the Landscape
• Chiral anomalies on a circle and their cancellation in F-theory
• Inflation Expels Runaways
• Kinetic Mixing at Strong Coupling
• The Geometry of SO(3), SO(5), and SO(6) models
• Ubiquity of non-geometry in heterotic compactifications
• Massive quiver matrix models for massive charged particles in AdS
• Spin(7)-manifolds in compactifications to four dimensions
• Supersymmetric Flux Compactifications and Calabi-Yau Modularity
• F-Theory on Spin(7) Manifolds: Weak-Coupling Limit
• Abelianization of BPS Quivers and the Refined Higgs Index
• Statistical coupling constants from hidden sector entanglement
• Finiteness for self-dual classes in integral variations of Hodge structure
• Effect of reheating on predictions following multiple-field inflation
• Universal Properties of Type IIB and F-theory Flux Compactifications at Large Complex Structure
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• The complex Liouville string: the worldsheet
• On the GUT scale of F-Theory SU(5)
• Higher Spin de Sitter Hilbert Space
• Holographic Perspectives On Models Of Moduli Stabilization In M-Theory
• Revisiting toric SU(3) structures
• Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua
• $\mathcal{I}$/$c$-Extremization in M/F-Duality
• F-theory and the Witten Index
• Neutrino mixing and mass hierarchy in Gaussian landscapes
• A new CY elliptic fibration and tadpole cancellation
• Higher Forms and Membranes in 4D Supergravities
• On ${\alpha }^{\prime }$-effects from $D$-branes in $4d\mathcal{N}=1$
• U-folds as K3 fibrations
• Three-form periods on Calabi-Yau fourfolds: Toric hypersurfaces and F-theory applications
• ${\alpha }^{\prime }$-Corrections and de Sitter Vacua - a Mirage?
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Calabi-Yau Manifolds and SU(3) Structure
• Gauge/gravity duality and the interplay of various fractional branes
• Revisiting arithmetic solutions to the $W=0$ condition
• Shift-symmetries and gauge coupling functions in orientifolds and F-theory
• On 'Light' Fermions and Proton Stability in 'Big Divisor' D3/D7 Swiss Cheese Phenomenology
• Towards Large Volume Big Divisor D3-D7 "mu-Split Supersymmetry" and Ricci-Flat Swiss-Cheese Metrics, and Dimension-Six Neutrino Mass Operators
• Twelve-dimensional Effective Action and T-duality
• Compact objects and the swampland
• Characteristic numbers of crepant resolutions of Weierstrass models
• Heterotic/Heterotic and Heterotic/F-theory Duality
• The String Landscape: On Formulas for Counting Vacua
• Type IIB Flux Vacua at Large Complex Structure
• F-theory Yukawa Couplings and Supersymmetric Quantum Mechanics
• Orientiholes
• Constraints on GUT 7-brane Topology in F-theory
• 3d N=1 effective supergravity and F-theory from M-theory on fourfolds
• SL(2,R) covariant conditions for N=1 flux vacua
• Exploring a simple sector of the Einstein-Maxwell landscape
• Orders of Vanishing and U(1) Charges in F-theory
• Lectures on Naturalness, String Landscape and Multiverse
• Tachyons in Throat Cosmology
• Type IIA Flux Vacua and ${\alpha }^{\prime }$-corrections
• MSSM-like from $S{U}_5\times D_4$ Models
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
• Phenomenological implications of a minimal F-theory GUT with discrete symmetry
• Toric manifolds for Flux compactification
• Constraints on heterotic M-theory from s-cobordism
• F-term Uplift in Heterotic M-theory
• 6d $\mathcal{N}=(1,0)$ anomalies on $S^1$ and F-theory implications
• F-theory Flux Vacua and Attractor Equations
• Topics in Supergravity Phenomenology
• Chronons in M-theory and F-theory
• Aspects of moduli stabilization in type IIB string theory
• Eight dimensional physics and the Langlands program - A short note