Geometric Singularities and Enhanced Gauge Symmetries

Abstract

Using ``Tate's algorithm,'' we identify loci in the moduli of F-theory compactifications corresponding to enhanced gauge symmetry. We apply this to test the proposed F-theory/heterotic dualities in six dimensions. We recover the perturbative gauge symmetry enhancements of the heterotic side and the physics of small $SO(32)$ instantons, and discover new mixed perturbative/non-perturbative gauge symmetry enhancements. Upon further toroidal compactification to 4 dimensions, we derive the chain of Calabi-Yau threefolds dual to various Coulomb branches of heterotic strings.

49 pages harvmac big (must print in big mode for tables to appear correctly); Typos and reference corrected

References in corpus (24)

• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• D-branes, Quivers, and ALE Instantons
• Massless Black Holes and Conifolds in String Theory
• Small Instantons in String Theory
• Consistency Conditions for Orientifolds and D-Manifolds
• Phase Transitions In M-Theory And F-Theory
• Exact Results for N=2 Compactifications of Heterotic Strings
• Comments on String Dynamics in Six Dimensions
• A Note on the Green - Schwarz Mechanism in Open - String Theories
• Two-Dimensional Black Hole and Singularities of CY Manifolds
• Some Comments On String Dynamics
• Small $E_8$ Instantons and Tensionless Non-critical Strings
• Integrable systems and supersymmetric gauge theory
• Nonperturbative Results on the Point Particle Limit of N=2 Heterotic String Compactifications
• Second-Quantized Mirror Symmetry
• Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory
• Evidence for Heterotic/Heterotic Duality
• D-Strings on D-Manifolds
• Anomaly-Free Supersymmetric Models in Six Dimensions
• Chains of N=2, D=4 heterotic/type II duals
• New Higgs Transitions between Dual N=2 String Models

Cited by in corpus (378)

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• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• Beauty is Attractive: Moduli Trapping at Enhanced Symmetry Points
• Calabi-Yau fourfolds for M- and F-Theory compactifications
• K3 Surfaces and String Duality
• F-Theory at Constant Coupling
• Lectures on F-theory compactifications and model building
• Les Houches Lectures on Constructing String Vacua
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• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
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• On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs
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• Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
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• Anomaly Equations and Intersection Theory
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• The Tate Form on Steroids: Resolution and Higher Codimension Fibers
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• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• Five-Brane Superpotentials and Heterotic/F-theory Duality
• Gauge-Mediated Supersymmetry Breaking in String Compactifications
• 4D Gauge Theories with Conformal Matter
• The Vertical, the Horizontal and the Rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications
• On Vector Bundles and Chiral Matter in N=1 Heterotic Compactifications
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• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• F-Theory and N=1 SCFTs in Four Dimensions
• A Note on Local GUT Models in F-Theory
• On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
• T-Branes at the Limits of Geometry
• Small resolutions of SU(5)-models in F-theory
• Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs
• A systematic search for anomaly-free supergravities in six dimensions
• Three Looks at Instantons in F-theory -- New Insights from Anomaly Inflow, String Junctions and Heterotic Duality
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• Tate Trees for Elliptic Fibrations with Rank one Mordell-Weil group
• F theory Vacua in Four Dimensions and Toric Threefolds
• F-theory and the Gimon-Polchinski Orientifold
• Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory, I
• Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality
• Notes on Supersymmetric Gauge Theories in Five and Six Dimensions
• Wavefunctions and the Point of E8 in F-theory
• Toric Elliptic Fibrations and F-Theory Compactifications
• Chiral matter wavefunctions in warped compactifications
• F-GUTs with Mordell-Weil U(1)'s
• Fluxed M5-instantons in F-theory
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
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• Rational F-Theory GUTs without exotics
• Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
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• 4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case
• On the global symmetries of 6D superconformal field theories
• Duality in String Theory
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• GUT Relations from String Theory Compactifications
• Mathieu Moonshine and N=2 String Compactifications
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• Enhanced Gauge Symmetry in Type II and F-Theory Compactifications: Dynkin Diagrams from Polyhedra
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
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• SU(3) x SU(2) x U(1) Vacua in F-Theory
• Discrete Symmetries in Heterotic/F-theory Duality and Mirror Symmetry
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• On the Complementarity of F-theory, Orientifolds, and Heterotic Strings
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• Towards a Realistic F-theory GUT
• Generic matter representations in 6D supergravity theories
• Three Dimensional N=2 Gauge Theories and Degenerations of Calabi-Yau Four-Folds
• Tate Form and Weak Coupling Limits in F-theory
• Searching for the Standard Model in the String Landscape : SUSY GUTs
• Calabi-Yau Spaces and Five Dimensional Field Theories with Exceptional Gauge Symmetry
• Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory
• Higgs Bundles for M-theory on $G_2$-Manifolds
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Heterotic T-fects, 6D SCFTs, and F-Theory
• Stable sheaves on elliptic fibrations
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• Flopping and Slicing: SO(4) and Spin(4)-models
• Exotic matter on singular divisors in F-theory
• Large U(1) charges in F-theory
• Tate's Algorithm for F-theory GUTs with two U(1)s
• Reconciling Grand Unification with Strings by Anisotropic Compactifications
• Theories of Class F and Anomalies
• The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
• On F-theory E_6 GUTs
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
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• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Learning non-Higgsable gauge groups in 4D F-theory
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• Discrete gauging and Hasse diagrams
• 5d SCFTs from $(E_n,E_m)$ Conformal Matter
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• Comments on A,B,C Chains of Heterotic and Type II Vacua
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• The Toric SO(10) F-Theory Landscape
• The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications
• Matter in transition
• Gauge Groups and Matter Fields on Some Models of F-theory without Section
• Quantum q-Langlands Correspondence
• The Geometry of SO(3), SO(5), and SO(6) models
• Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions
• The discrete Green-Schwarz mechanism in 6D F-Theory and Elliptic Genera of Non-Critical Strings
• Non-simply-laced Lie algebras via F theory strings
• String Vacua with N=2 Supersymmetry in Four Dimensions
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• ICMP lecture on Heterotic/F-theory duality
• Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications
• N=1 Dual String Pairs and their Massless Spectra
• F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces
• On Singular Fibres in F-Theory
• F-theory and linear sigma models
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Weak Mixing Angle and Proton Stability in F-theory GUT
• F-theory duals of singular heterotic K3 mode
• On the GUT scale of F-Theory SU(5)
• String Duality and Enumeration of Curves by Jacobi Forms
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• A Terminal Velocity on the Landscape: Particle Production near Extra Species Loci in Higher Dimensions
• The quiver approach to the BPS spectrum of a 4d N=2 gauge theory
• Building SO(10) models from F-theory
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua
• Seiberg-Witten Theory and Calogero-Moser Systems
• F-theory and the Witten Index
• On Global Flipped SU(5) GUTs in F-theory
• Anomalies as Obstructions: from Dimensional Lifts to Swampland
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• Gauge/Gravity Duality in Heterotic String Theory
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• Supersymmetric three family chiral SU(6) grand unification model from F-theory
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Extended Gauge Symmetries in F-theory
• Automatic Enhancement in 6D Supergravity and F-theory Models
• D=6, N=1 String Vacua and Duality
• Aspects of F-Theory GUTs
• U(n) Spectral Covers from Decomposition
• Box Graphs and Resolutions I
• 6d/5d exceptional gauge theories from web diagrams
• Exact solutions for some N=2 supersymmetric SO(N) gauge theories with vectors and spinors
• On the Standard Model Group in F-theory
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• Hunting for the New Symmetries in Calabi-Yau Jungles
• Classifying Global Symmetries of 6D SCFTs
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Characteristic numbers of elliptic fibrations with non-trivial Mordell-Weil groups
• Toward the Gravity Dual of Heterotic Small Instantons
• Weak Coupling, Degeneration and Log Calabi-Yau Spaces
• Calabi-Yau Duals for CHL Strings
• Enhanced Preheating after Multi-Field Inflation: On the Importance of being Special
• Generic construction of the Standard Model gauge group and matter representations in F-theory
• $6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
• Equivalent String Networks and Uniqueness of BPS States
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• Bootstrapping (D, D) Conformal Matter
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• Exact Solutions of Exceptional Gauge Theories from Toric Geometry
• The Ruled Vertex and D-E Degenerations
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• K3 metrics from little string theory
• Gauge symmetry breaking with fluxes and natural Standard Model structure from exceptional GUTs in F-theory
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• Local Grand Unification in the Heterotic Landscape
• Anomaly-Free Supergravities in Six Dimensions
• Large U(1) charges from flux breaking in 4D F-theory models
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• Supersymmetric Wilson Loops, Instantons, and Deformed $\mathcal{W}$-Algebras
• Transitions of Orbifold Vacua
• SCFTs, Holography, and Topological Strings
• Stringy Cosmic Strings and Compactifications of F-theory
• Jacobi Forms of Higher Index and Paramodular Groups in N=2, D=4 Compactifications of String Theory
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• String Model Building
• W=0 Complex Structure Moduli Stabilization on CM-type K3 x K3 Orbifolds:---Arithmetic, Geometry and Particle Physics---
• Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations
• N=1 Dual String Pairs and their Modular Superpotentials
• On Building superpotentials in F- GUTs
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
• Orders of Vanishing and U(1) Charges in F-theory
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
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• The origin of discrete symmetries in F-theory models
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• Discrete Wilson Lines in F-Theory
• Flops and Fibral Geometry of E${}_7$-models
• Abelian gauge symmetries and fluxed instantons in compactifications of type IIB and F-theory
• Non-split singularities and conifold transitions in F-theory
• Introduction to String Theory
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• Gluino Condensation in F-theory
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• Reflexive Numbers and Berger Graphs from Calabi-Yau Spaces
• Matrix Factorizations for Local F-Theory Models
• A Large N Type IIB Duality via a Spin(7) Geometric Transition as an F-theory Flop
• Weyl Mutations in Quiver Yangians
• Reflexions on Mahler: Dessins, Modularity and Gauge Theories
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• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations