Matter and singularities

Abstract

We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the geometry associated with several types of singularities and the associated matter representations. We also construct global F-theory models for 6D and 4D theories containing these matter representations. The codimension two singularities encountered include examples where the apparent Kodaira singularity type does not need to be completely resolved to produce a smooth Calabi-Yau, examples with rank enhancement by more than one, and examples where the 7-brane configuration is singular. We identify novel phase transitions, in some of which the gauge group remains fixed but the singularity type and associated matter content change along a continuous family of theories. Global analysis of 6D theories on P^2 with 7-branes wrapped on curves of small degree reproduces the range of 6D supergravity theories identified through anomaly cancellation and other consistency conditions. Analogous 4D models are constructed through global F-theory compactifications on P^3, and have a similar pattern of SU(N) matter content. This leads to a constraint on the matter content of a limited class of 4D supergravity theories containing SU(N) as a local factor of the gauge group.

55 pages, 7 figures; v2: references added; v3: minor correction

References in corpus (11)

• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• Lectures on F-theory compactifications and model building
• Les Houches Lectures on Constructing String Vacua
• T-Branes and Monodromy
• Global aspects of the space of 6D N = 1 supergravities
• The N=1 effective action of F-theory compactifications
• Tate's algorithm and F-theory
• Charge Lattices and Consistency of 6D Supergravity
• 6D supergravity without tensor multiplets
• TASI Lectures on Supergravity and String Vacua in Various Dimensions
• Small resolutions of SU(5)-models in F-theory

Cited by in corpus (95)

• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Classifying bases for 6D F-theory models
• Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
• G_4 flux, chiral matter and singularity resolution in F-theory compactifications
• F-theory fluxes, Chirality and Chern-Simons theories
• Anomaly Equations and Intersection Theory
• Toric bases for 6D F-theory models
• Six-dimensional (1,0) effective action of F-theory via M-theory on Calabi-Yau threefolds
• SU(5) Tops with Multiple U(1)s in F-theory
• F-theory and the Classification of Little Strings
• Box Graphs and Singular Fibers
• The Tate Form on Steroids: Resolution and Higher Codimension Fibers
• On the Hodge structure of elliptically fibered Calabi-Yau threefolds
• 6D supergravity without tensor multiplets
• Gauge Fluxes in F-theory and Type IIB Orientifolds
• Matter From Geometry Without Resolution
• Three-Family Particle Physics Models from Global F-theory Compactifications
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure
• Scanning the skeleton of the 4D F-theory landscape
• Non-Higgsable clusters for 4D F-theory models
• Calabi-Yau threefolds with large h^{2, 1}
• The frozen phase of F-theory
• ${\mathbb{P}}^1$-bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
• A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
• F-theory and 2d (0,2) Theories
• Geometric constraints in dual F-theory and heterotic string compactifications
• Structure in 6D and 4D N=1 supergravity theories from F-theory
• A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds
• Seiberg-Witten Geometries Revisited
• Small resolutions of SU(5)-models in F-theory
• Gauge Backgrounds and Zero-Mode Counting in F-Theory
• Toric Elliptic Fibrations and F-Theory Compactifications
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• On the global symmetries of 6D superconformal field theories
• Generic matter representations in 6D supergravity theories
• Tate Form and Weak Coupling Limits in F-theory
• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• Higgs Bundles for M-theory on $G_2$-Manifolds
• Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• Exotic matter on singular divisors in F-theory
• Large U(1) charges in F-theory
• Three-Index Symmetric Matter Representations of SU(2) in F-Theory from Non-Tate Form Weierstrass Models
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Learning non-Higgsable gauge groups in 4D F-theory
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Singular Geometry and Higgs Bundles in String Theory
• GUT theories from Calabi-Yau 4-folds with SO(10) Singularities
• Mordell-Weil Torsion, Anomalies, and Phase Transitions
• Gauge Groups and Matter Fields on Some Models of F-theory without Section
• The Geometry of SO(3), SO(5), and SO(6) models
• Matter in transition
• New Global F-theory GUTs with U(1) symmetries
• Gauge groups and matter spectra in F-theory compactifications on genus-one fibered Calabi-Yau 4-folds without section - hypersurface and double cover constructions
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• 6D SCFTs and Gravity
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• The Geometry of F${}_4$-Models
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• Aspects of F-Theory GUTs
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• Automatic Enhancement in 6D Supergravity and F-theory Models
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• Classifying Global Symmetries of 6D SCFTs
• Incidence Geometry in a Weyl Chamber I: $G{L}_n$
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• $6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• 48 Crepant Paths to $\text{SU}(2)\times \text{SU}(3)$
• On finiteness of Type IIB compactifications: Magnetized branes on elliptic Calabi-Yau threefolds
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• Magic square and half-hypermultiplets in F-theory
• Half-hypermultiplets and incomplete/complete resolutions in F-theory
• SCFTs, Holography, and Topological Strings
• Orders of Vanishing and U(1) Charges in F-theory
• Faking Gauge Coupling Unification in String Theory
• Anomaly-free Multiple Singularity Enhancement in F-theory
• Matter representations from geometry: under the spell of Dynkin
• Affine characters at negative level and elliptic genera of non-critical strings
• 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
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• Non-split singularities and conifold transitions in F-theory
• Intersecting brane models and F-theory in six dimensions
• Abelian gauge symmetries and fluxed instantons in compactifications of type IIB and F-theory
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape