F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections

Abstract

We study elliptic fibrations for F-theory compactifications realizing 4d and 6d supersymmetric gauge theories with abelian gauge factors. In the fibration these U(1) symmetries are realized in terms of additional rational sections. We obtain a universal characterization of all the possible U(1) charges of matter fields by determining the corresponding codimension two fibers with rational sections. In view of modelling supersymmetric Grand Unified Theories, one of the main examples that we analyze are U(1) symmetries for SU(5) gauge theories with \bar{5} and 10 matter. We use a combination of constraints on the normal bundle of rational curves in Calabi-Yau three- and four-folds, as well as the splitting of rational curves in the fibers in codimension two, to determine the possible configurations of smooth rational sections. This analysis straightforwardly generalizes to multiple U(1)s. We study the flops of such fibers, as well as some of the Yukawa couplings in codimension three. Furthermore, we carry out a universal study of the U(1)-charged GUT singlets, including their KK-charges, and determine all realizations of singlet fibers. By giving vacuum expectation values to these singlets, we propose a systematic way to analyze the Higgsing of U(1)s to discrete gauge symmetries in F-theory.

93 pages, 23 figures

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Cited by in corpus (46)

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• Terminal Singularities, Milnor Numbers, and Matter in F-theory
• Swampland Bounds on the Abelian Gauge Sector
• General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure
• F-theory and 2d (0,2) Theories
• 6d SCFTs and U(1) Flavour Symmetries
• General Prescription for Global U(1)'s in 6D SCFTs
• Tall sections from non-minimal transformations
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
• An F-theory Realization of the Chiral MSSM with ${\mathbb{Z}}_2$-Parity
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• Large U(1) charges in F-theory
• Discrete gauge groups in certain F-theory models in six dimensions
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Statistics of Flux Vacua for Particle Physics
• Tuned and Non-Higgsable U(1)s in F-theory
• The Toric SO(10) F-Theory Landscape
• High electric charges in M-theory from quiver varieties
• Modular Curves and Mordell-Weil Torsion in F-theory
• Non-Abelian discrete gauge symmetries in F-theory
• Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications
• F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Global tensor-matter transitions in F-theory
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• Infinitely many 4d N=1 SCFTs with a=c
• K3 surfaces without section as double covers of Halphen surfaces, and F-theory compactifications
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• A 5d perspective on the compactifications of 6d SCFTs to 4d $\mathcal{N}=1$ SCFTs
• Large U(1) charges from flux breaking in 4D F-theory models
• Heterotic-$\mathbf{F}$-theory Duality with Wilson Line Symmetry-breaking
• Orders of Vanishing and U(1) Charges in F-theory
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
• Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• A note on transition in discrete gauge groups in F-theory
• A dessin on the base: a description of mutually non-local 7-branes without using branch cuts