Classifying bases for 6D F-theory models

Abstract

We classify six-dimensional F-theory compactifications in terms of simple features of the divisor structure of the base surface of the elliptic fibration. This structure controls the minimal spectrum of the theory. We determine all irreducible configurations of divisors ("clusters") that are required to carry nonabelian gauge group factors based on the intersections of the divisors with one another and with the canonical class of the base. All 6D F-theory models are built from combinations of these irreducible configurations. Physically, this geometric structure characterizes the gauge algebra and matter that can remain in a 6D theory after maximal Higgsing. These results suggest that all 6D supergravity theories realized in F-theory have a maximally Higgsed phase in which the gauge algebra is built out of summands of the types su(3), so(8), f_4, e_6, e_8, e_7, (g_2 + su(2)), and su(2) + so(7) + su(2), with minimal matter content charged only under the last three types of summands, corresponding to the non-Higgsable cluster types identified through F-theory geometry. Although we have identified all such geometric clusters, we have not proven that there cannot be an obstruction to Higgsing to the minimal gauge and matter configuration for any possible F-theory model. We also identify bounds on the number of tensor fields allowed in a theory with any fixed gauge algebra; we use this to bound the size of the gauge group (or algebra) in a simple class of F-theory bases.

28 pages, 2 figures, 1 appendix. v2: added references, minor changes; v3: two signs corrected

References in corpus (7)

• Les Houches Lectures on Constructing String Vacua
• Global aspects of the space of 6D N = 1 supergravities
• Anomaly Equations and Intersection Theory
• Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds
• 6D supergravity without tensor multiplets
• TASI Lectures on Supergravity and String Vacua in Various Dimensions
• D5 elliptic fibrations: non-Kodaira fibers and new orientifold limits of F-theory

Cited by in corpus (102)

• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• 6d Conformal Matter
• Tensionless Strings and the Weak Gravity Conjecture
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• On the Defect Group of a 6D SCFT
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Toric bases for 6D F-theory models
• Physics of F-theory compactifications without section
• Strings of Minimal 6d SCFTs
• F-theory and the Classification of Little Strings
• 6D RG Flows and Nilpotent Hierarchies
• On the Hodge structure of elliptically fibered Calabi-Yau threefolds
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Three-Family Particle Physics Models from Global F-theory Compactifications
• Swampland Bounds on the Abelian Gauge Sector
• Matter From Geometry Without Resolution
• A New Construction of Calabi-Yau Manifolds: Generalized CICYs
• Anomaly of strings of 6d $\mathcal{N}=(1,0)$ theories
• 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
• Fission, Fusion, and 6D RG Flows
• 6D Fractional Quantum Hall Effect
• 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
• Geometric constraints in dual F-theory and heterotic string compactifications
• 6d SCFTs and U(1) Flavour Symmetries
• 4D Gauge Theories with Conformal Matter
• Gauged 2-form Symmetries in 6D SCFTs Coupled to Gravity
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• UV Completions for Non-Critical Strings
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• TASI Lectures on F-theory
• Fine Tuning, Sequestering, and the Swampland
• Blowup Equations for 6d SCFTs. I
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• IIB Explored: Reflection 7-Branes
• General Prescription for Global U(1)'s in 6D SCFTs
• T-Branes, String Junctions, and 6D SCFTs
• From 6D SCFTs to Dynamic GLSMs
• 6d strings from new chiral gauge theories
• 6d $\mathcal{N}=(1,0)$ theories on $S^1/T^2$ and class S theories: part II
• The string landscape and low energy supersymmetry
• Dual Little Strings and their Partition Functions
• Generic matter representations in 6D supergravity theories
• 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
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• On Axion Reheating in the String Landscape
• 6d strings and exceptional instantons
• Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• Surface defects in E-string compactifications and the van Diejen model
• On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• Learning non-Higgsable gauge groups in 4D F-theory
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Statistics of Flux Vacua for Particle Physics
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Tuned and Non-Higgsable U(1)s in F-theory
• Singular Geometry and Higgs Bundles in String Theory
• The Toric SO(10) F-Theory Landscape
• The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications
• On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds
• The Geometry of SO(3), SO(5), and SO(6) models
• From strings in 6d to strings in 5d
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• On the Scarcity of Weak Coupling in the String Landscape
• 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
• Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua
• The Geometry of F${}_4$-Models
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Automatic Enhancement in 6D Supergravity and F-theory Models
• Higgsing towards E-strings
• Classifying Global Symmetries of 6D SCFTs
• Fibration structure in toric hypersurface Calabi-Yau threefolds
• Mirror symmetry and elliptic Calabi-Yau manifolds
• 48 Crepant Paths to $\text{SU}(2)\times \text{SU}(3)$
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• On the Elliptic Calabi-Yau Fourfold with Maximal $h^{1,1}$
• Magic square and half-hypermultiplets in F-theory
• SCFTs, Holography, and Topological Strings
• Orders of Vanishing and U(1) Charges in F-theory
• Complete Intersection Fibers in F-Theory
• Evidence for C-theorems in 6D SCFTs
• Matter representations from geometry: under the spell of Dynkin
• On the Tropical Discs Counting on Elliptic K3 Surfaces with General Singular Fibres
• Intersecting brane models and F-theory in six dimensions
• EFT of 6D SUSY RG Flows
• Domain walls and M2-branes partition functions: M-theory and ABJM Theory
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Aspects of 4d supersymmetric dynamics and geometry
• Spectral Covers, Integrality Conditions, and Heterotic/F-theory Duality