Compactifications of F-Theory on Calabi--Yau Threefolds -- I

Abstract

We study compactifications of F-theory on certain Calabi--Yau threefolds. We find that $N=2$ dualities of type II/heterotic strings in 4 dimensions get promoted to $N=1$ dualities between heterotic string and F-theory in 6 dimensions. The six dimensional heterotic/heterotic duality becomes a classical geometric symmetry of the Calabi--Yau in the F-theory setup. Moreover the F-theory compactification sheds light on the nature of the strong coupling transition and what lies beyond the transition at finite values of heterotic string coupling constant.

24 pages + 1 figure. Minor corrections and reference added; final version to appear in Nuclear Physics B

Cited by in corpus (449)

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• D7-Brane Motion from M-Theory Cycles and Obstructions in the Weak Coupling Limit
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• String Universality and Non-Simply-Connected Gauge Groups in 8d
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• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
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• Colliding Singularities in F-theory and Phase Transitions
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• Calabi-Yau 4-folds and toric fibrations
• Pixelated Dark Energy
• The Mirror Transform of Type I Vacua in Six Dimensions
• General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Scanning the skeleton of the 4D F-theory landscape
• Non-Higgsable clusters for 4D F-theory models
• Modular Symmetries and the Swampland Conjectures
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• The F-theory geometry with most flux vacua
• Holomorphic Couplings in String Theory
• Non-Perturbative Heterotic D=6,4 Orbifold Vacua
• The frozen phase of F-theory
• 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
• Conformal Aspects of Spinor-Vector Duality
• 8d gauge anomalies and the topological Green-Schwarz mechanism
• E + E $\to$ H
• A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
• F-theory and 2d (0,2) Theories
• On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups
• Geometric constraints in dual F-theory and heterotic string compactifications
• Codimension-2 Brane-Bulk Matching: Examples from Six and Ten Dimensions
• On Exceptional Instanton Strings
• The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification
• A Note on G-Fluxes for F-theory Model Building
• A Note on Orientifolds and F-theory
• Structure in 6D and 4D N=1 supergravity theories from F-theory
• A Minimal Superstring Standard Model I: Flat Directions
• The anomaly that was not meant IIB
• Elevating the Free-Fermion $Z_2\times Z_2$ Orbifold Model to a Compactification of F-Theory
• Chiral 2d Theories from N=4 SYM with Varying Coupling
• Phases, Flops and F-theory: SU(5) Gauge Theories
• Non-Critical Strings, Del Pezzo Singularities And Seiberg-Witten Curves
• Anomaly Cancelation in Field Theory and F-theory on a Circle
• Five-Brane Superpotentials and Heterotic/F-theory Duality
• Higher derivatives in Type II and M-theory on Calabi-Yau threefolds
• Topological duality twist and brane instantons in F-theory
• A Class of N=1 Dual String Pairs and its Modular Superpotential
• TeV-scale Supersymmetric Standard Model and Brane World
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• String theory dualities from M theory
• Fixing D7 Brane Positions by F-Theory Fluxes
• Duality in Heterotic Vacua With Four Supercharges
• Disorder Averaging and its UV (Dis)Contents
• Landau-Ginzburg Vacua of String, M- and F-Theory at c=12
• Multiple Realisations of N=1 Vacua in Six Dimensions
• Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
• F Theory Orientifolds, M Theory Orientifolds, and Twisted Strings
• Fluxes in F-theory Compactifications on Genus-One Fibrations
• Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• Completeness in supergravity constructions
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• Collider Signatures from the Brane World
• F theory Vacua in Four Dimensions and Toric Threefolds
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• F-theory and the Gimon-Polchinski Orientifold
• Triality in Little String Theories
• Notes on Supersymmetric Gauge Theories in Five and Six Dimensions
• General Prescription for Global U(1)'s in 6D SCFTs
• Chiral matter wavefunctions in warped compactifications
• IIB Explored: Reflection 7-Branes
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• F-theory, SO(32) and Toric Geometry
• Tall sections from non-minimal transformations
• Mordell-Weil Lattice via String Junctions
• Black Holes and Flop Transitions in M-Theory on Calabi-Yau Threefolds
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Rational F-Theory GUTs without exotics
• Dual Little Strings from F-Theory and Flop Transitions
• Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
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• The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
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• Bubbling Orientifolds
• On Condensation of Closed-string Tachyons
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• On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
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• Type II string theory and modularity
• Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models
• Enriques and Octonionic Magic Supergravity Models
• Generic matter representations in 6D supergravity theories
• A Test Of The Chiral E8 Current Algebra On A 6D Non-Critical String
• Calabi-Yau Spaces and Five Dimensional Field Theories with Exceptional Gauge Symmetry
• Orientifold Limit of F-theory Vacua
• Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory
• Strong Coupling in F-theory and Geometrically Non-Higgsable Seven-branes
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Tate Form and Weak Coupling Limits in F-theory
• Unification of M- and F- Theory Calabi-Yau Fourfold Vacua
• On Brane Back-Reaction and de Sitter Solutions in Higher-Dimensional Supergravity
• The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
• Six line configurations and string dualities
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Effective Actions near Singularities
• Stable sheaves on elliptic fibrations
• 6d strings and exceptional instantons
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Non-Simply-Connected Symmetries in 6D SCFTs
• On Tensionless Strings in $3+1$ Dimensions
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• Theories of Class F and Anomalies
• On F-theory E_6 GUTs
• Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory
• The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
• Large U(1) charges in F-theory
• Flopping and Slicing: SO(4) and Spin(4)-models
• Unification of String Dualities
• Resolving spacetime singularities in flux compactifications & KKLT
• Exotic matter on singular divisors in F-theory
• Tate's Algorithm for F-theory GUTs with two U(1)s
• Complex/Symplectic Mirrors
• Discrete gauge groups in certain F-theory models in six dimensions
• Three-Index Symmetric Matter Representations of SU(2) in F-Theory from Non-Tate Form Weierstrass Models
• Orientifold and F-theory Duals of CHL Strings
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• Modular Subgroups, Dessins d'Enfants and Elliptic K3 Surfaces
• Learning non-Higgsable gauge groups in 4D F-theory
• A Non-perturbative Description of the Gimon-Polchinski Orientifold
• Towards the MSSM from F-theory
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Tuned and Non-Higgsable U(1)s in F-theory
• Euler Characteristics of Crepant Resolutions of Weierstrass Models
• F-theory Family Unification
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• Comments on A,B,C Chains of Heterotic and Type II Vacua
• The BPS spectrum of the 4d N=2 SCFT's H_1, H_2, D_4, E_6, E_7, E_8
• On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
• The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications
• High electric charges in M-theory from quiver varieties
• The Toric SO(10) F-Theory Landscape
• Abelian Gauge Fluxes and Local Models in F-Theory
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Gauge Groups and Matter Fields on Some Models of F-theory without Section
• BPS Solutions of Six-Dimensional (1,0) Supergravity Coupled to Tensor Multiplets
• Supersymmetry Breaking and the Cosmological Constant
• Mirror Symmetry via Deformation of Bundles on K3 Surfaces
• On Quantum Special Kaehler Geometry
• Ubiquity of non-geometry in heterotic compactifications
• Spin(7)-manifolds in compactifications to four dimensions
• Matter in transition
• String Vacua with N=2 Supersymmetry in Four Dimensions
• Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions
• Heterotic-Type IIA Duality and Degenerations of K3 Surfaces
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• N=1 Dual String Pairs and their Massless Spectra
• Indices for 6 dimensional superconformal field theories
• Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• E_8 x E_8 Small Instantons in Matrix Theory
• Aspects of (0,2) Orbifolds and Mirror Symmetry
• Nonperturbative flipped SU(5) vacua in heterotic M-theory
• F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• Four-dimensional black hole entropy from F-theory
• Root Bundles and Towards Exact Matter Spectra of F-theory MSSMs
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• F-theory and linear sigma models
• F-theory duals of singular heterotic K3 mode
• An Index for Ray Operators in 5d $E_n$ SCFTs
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Tools for CICYs in F-theory
• Modularity from Monodromy
• D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds
• Black String Entropy and Fourier-Mukai Transform
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• K3-fibered Calabi-Yau threefolds I, the twist map
• Anomalies as Obstructions: from Dimensional Lifts to Swampland
• On Global Flipped SU(5) GUTs in F-theory
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• Enhanced supersymmetry from vanishing Euler number
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Excision of Singularities by Stringy Domain Walls
• F-theory and the Witten Index
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• Towards a complete classification of 6D supergravities
• D=6, N=1 String Vacua and Duality
• Expanding F-Theory
• Extended Gauge Symmetries in F-theory
• Horizon Geometry, Duality and Fixed scalars in Six Dimensions
• Supergravity in Twelve Dimension
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Gauge/Gravity Duality in Heterotic String Theory
• Automatic Enhancement in 6D Supergravity and F-theory Models
• Light Strings and Strong Coupling in F-theory
• Statistics of Limit Root Bundles Relevant for Exact Matter Spectra of F-Theory MSSMs
• Exact solutions for some N=2 supersymmetric SO(N) gauge theories with vectors and spinors
• U(n) Spectral Covers from Decomposition
• Gauged supergravities and their symmetry-breaking vacua in F-theory
• NS5-Branes and Line Bundles in Heterotic/F-Theory Duality
• 6d/5d exceptional gauge theories from web diagrams
• On the Standard Model Group in F-theory
• Holomorphic Couplings In Non-Perturbative String Compactifications
• The Fate of Discrete 1-Form Symmetries in 6d
• Calabi-Yau Duals for CHL Strings
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• Classifying Global Symmetries of 6D SCFTs
• Mirror Symmetry and Landau Ginzburg Calabi-Yau Superpotentials in F-theory Compactifications
• Fibration structure in toric hypersurface Calabi-Yau threefolds
• Calabi-Yau Geometries: Algorithms, Databases, and Physics
• F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
• More on a dessin on the base: Kodaira exceptional fibers and mutually (non-)local branes
• D-Branes and Twelve Dimensions
• Brill-Noether-general Limit Root Bundles: Absence of vector-like Exotics in F-theory Standard Models
• Mirror symmetry and elliptic Calabi-Yau manifolds
• Bound states of spinning black holes in five dimensions
• New N=1 Supersymmetric 3-dimensional Superstring Vacua from U-manifolds
• Generic construction of the Standard Model gauge group and matter representations in F-theory
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• Modular Forms as Classification Invariants of 4D N=2 Heterotic--IIA Dual Vacua
• Dualities and phase transitions for Calabi-Yau 3folds and 4folds
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• Heterotic-Type II duality in the hypermultiplet sector
• From Type II string theory towards BSM/dark sector physics
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• Heterotic M(atrix) theory at generic points in Narain moduli space
• A Note on Non-Flat Points in the $SU(5)\times U(1)$ PQ F-Theory Model
• Heterotic/Heterotic and Heterotic/F-theory Duality
• Natural F-theory constructions of Standard Model structure from $E_7$ flux breaking
• Matter from Toric Geometry
• String-String triality for d=4, Z_2 orbifolds
• On the Elliptic Calabi-Yau Fourfold with Maximal $h^{1,1}$
• Weyl invariant Jacobi forms along Higgsing trees
• Intersecting D7-Branes, I5-Branes and Conifolds
• Exact Solutions of Exceptional Gauge Theories from Toric Geometry
• Non-perturbative K3 Orientifolds with NS-NS B-flux
• Extremal Bundles on Calabi-Yau Threefolds
• F-theory Yukawa Couplings and Supersymmetric Quantum Mechanics
• Non-Geometric Vacua of the $\text{Spin}(32)/{\mathbb{Z}}_2$ Heterotic String and Little String Theories
• Generating functions for intersection products of divisors in resolved F-theory models
• Phenomenology with F-theory SU(5)
• Constraints on GUT 7-brane Topology in F-theory
• Structure of stable degeneration of K3 surfaces into pairs of rational elliptic surfaces
• Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory
• The Large N Limit of $\mathcal{N}=1$ Field Theories from F Theory
• Magic square and half-hypermultiplets in F-theory
• Nikulin involutions and the CHL string
• Extending the Geometry of Heterotic Spectral Cover Constructions
• Large U(1) charges from flux breaking in 4D F-theory models
• The Master Equation for the Prepotential-Pub
• Constructing and Machine Learning Calabi-Yau Five-folds
• Special Geometry and Automorphic Forms
• Atomic Higgsings of 6D SCFTs
• Transitions of Orbifold Vacua
• Stringy Cosmic Strings and Compactifications of F-theory
• Heterotic String Compactification and New Vector Bundles
• Type I on (Generalized) Voisin-Borcea Orbifolds and Non-perturbative Orientifolds
• Bootstrapping ADE M-strings
• Orders of Vanishing and U(1) Charges in F-theory
• N=1 Dual String Pairs and their Modular Superpotentials
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
• Strings on Calabi--Yau spaces and Toric Geometry
• Atomic Higgsings of 6D SCFTs II: Induced Flows
• Orbifolds of M-Theory and Type II String Theories in Two Dimensions
• Puzzles on the Duality between Heterotic and Type IIA Strings
• Anatomy of a Duality
• Improved statistics for F-theory standard models
• Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds
• Towards natural and realistic $E_7$ GUTs in F-theory
• Faking Gauge Coupling Unification in String Theory
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Del Pezzo singularities and SUSY breaking
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• A dessin on the base: a description of mutually non-local 7-branes without using branch cuts
• A note on transition in discrete gauge groups in F-theory
• Six-dimensional origin of gravity mediated brane to brane supersymmetry breaking
• On the duality of F-theory and the CHL string in seven dimensions
• Affine characters at negative level and elliptic genera of non-critical strings
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
• Non-split singularities and conifold transitions in F-theory
• BPS index and 4d N=2 superconformal field theories
• On effective field theory of F-theory beyond leading order
• On M-theory on Real Toric Fibrations
• Singular Yukawa and gauge couplings in d=4 Heterotic String Vacua
• 6d $\mathcal{N}=(1,0)$ anomalies on $S^1$ and F-theory implications
• Intersecting brane models and F-theory in six dimensions
• Orientifold limits of singular $F$-theory vacua
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification (String Math 2022 Proceedings)
• Root bundles: Applications to F-theory Standard Models
• Chern-Simons couplings, modular duality, and anomaly cancellation in abelian F-theory
• Extremal Transitions in Heterotic String Theory
• The target space geometry of N=(2,1) string theory
• On Orientifold Constructions of Type IIA Dual Pairs
• Novel field theory phenomena from F theory and D-branes
• Graded Geometric Structures Underlying F-Theory Related Defect Theories
• Mirror Symmetry and the Web of Landau-Ginzburg String Vacua
• A Perfectoid Duality Between M-Theory and F-Theory
• Non-perturbative N=1 strings from geometric singularities