F-Theory Compactifications with Multiple U(1)-Factors: Constructing Elliptic Fibrations with Rational Sections

Abstract

We study F-theory compactifications with U(1)xU(1) gauge symmetry on elliptically fibered Calabi-Yau manifolds with a rank two Mordell-Weil group. We find that the natural presentation of an elliptic curve E with two rational points and a zero point is the generic Calabi-Yau onefold in dP_2. We determine the birational map to its Tate and Weierstrass form and the coordinates of the two rational points in Weierstrass form. We discuss its resolved elliptic fibrations over a general base B and classify them in the case of B=P^2. A thorough analysis of the generic codimension two singularities of these elliptic Calabi-Yau manifolds is presented. This determines the general U(1)xU(1)-charges of matter in corresponding F-theory compactifications. The matter multiplicities for the fibration over P^2 are determined explicitly and shown to be consistent with anomaly cancellation. Explicit toric examples are constructed, both with U(1)xU(1) and SU(5)xU(1)xU(1) gauge symmetry. As a by-product, we prove the birational equivalence of the two elliptic fibrations with elliptic fibers in the two blow-ups Bl_(1,0,0)P^2(1,2,3) and Bl_(0,1,0)P^2(1,1,2) employing birational maps and extremal transitions.

68 pages, 5 figures, 3 tables; v2: minor changes, 1 figure added; v3: typos corrected, references added

References in corpus (14)

• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• Lectures on F-theory compactifications and model building
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs
• The N=1 effective action of F-theory compactifications
• Models of Particle Physics from Type IIB String Theory and F-theory: A Review
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• Anomaly Cancellation And Abelian Gauge Symmetries In F-theory
• Higgs Bundles and UV Completion in F-Theory
• U(1) symmetries in F-theory GUTs with multiple sections
• The Tate Form on Steroids: Resolution and Higher Codimension Fibers
• Elliptic fibrations for SU(5) x U(1) x U(1) F-theory vacua
• Hypercharge Flux, Exotics, and Anomaly Cancellation in F-theory GUTs
• Massive U(1)s and Heterotic Five-Branes on K3

Cited by in corpus (91)

• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• A Stringy Test of the Scalar Weak Gravity Conjecture
• Refined stable pair invariants for E-, M- and [p,q]-strings
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Geometric Engineering in Toric F-Theory and GUTs with U(1) Gauge Factors
• Physics of F-theory compactifications without section
• SU(5) Tops with Multiple U(1)s in F-theory
• F-theory on Genus-One Fibrations
• Elliptic Fibrations with Rank Three Mordell-Weil Group: F-theory with U(1) x U(1) x U(1) Gauge Symmetry
• Discrete Gauge Symmetries by Higgsing in four-dimensional F-Theory Compactifications
• Box Graphs and Singular Fibers
• Yukawas and discrete symmetries in F-theory compactifications without section
• F-Theory Vacua with Z_3 Gauge Symmetry
• The Global Gauge Group Structure of F-theory Compactification with U(1)s
• F-Theory Compactifications with Multiple U(1)-Factors: Addendum
• Matter From Geometry Without Resolution
• Three-Family Particle Physics Models from Global F-theory Compactifications
• General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure
• The fate of U(1)'s at strong coupling in F-theory
• Calabi-Yau threefolds with large h^{2, 1}
• F-theory and All Things Rational: Surveying U(1) Symmetries with Rational Sections
• F-theory and 2d (0,2) Theories
• Geometric constraints in dual F-theory and heterotic string compactifications
• Computational Complexity of Vacua and Near-Vacua in Field and String Theory
• Anomaly Cancelation in Field Theory and F-theory on a Circle
• A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations
• Special Points of Inflation in Flux Compactifications
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• G4-Flux and Standard Model Vacua in F-theory
• Fluxes in F-theory Compactifications on Genus-One Fibrations
• F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• General Prescription for Global U(1)'s in 6D SCFTs
• F-GUTs with Mordell-Weil U(1)'s
• Tall sections from non-minimal transformations
• Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
• The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Rational F-Theory GUTs without exotics
• Chow groups, Deligne cohomology and massless matter in F-theory
• Towards the Standard Model in F-theory
• Discrete Symmetries in Heterotic/F-theory Duality and Mirror Symmetry
• Generic matter representations in 6D supergravity theories
• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• Discrete Gauge Groups in F-theory Models on Genus-One Fibered Calabi-Yau 4-folds without Section
• Discrete Family Symmetry from F-Theory GUTs
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• Tate's Algorithm for F-theory GUTs with two U(1)s
• The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case
• Three-Index Symmetric Matter Representations of SU(2) in F-Theory from Non-Tate Form Weierstrass Models
• Discrete gauge groups in certain F-theory models in six dimensions
• On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Tuned and Non-Higgsable U(1)s in F-theory
• Statistics of Flux Vacua for Particle Physics
• The Toric SO(10) F-Theory Landscape
• Modular Curves and Mordell-Weil Torsion in F-theory
• Gauge Groups and Matter Fields on Some Models of F-theory without Section
• Non-Cartan Mordell-Weil lattices of rational elliptic surfaces and heterotic/F-theory compactifications
• Gauge groups and matter spectra in F-theory compactifications on genus-one fibered Calabi-Yau 4-folds without section - hypersurface and double cover constructions
• Non-Abelian discrete gauge symmetries in F-theory
• F-theory models on K3 surfaces with various Mordell-Weil ranks -constructions that use quadratic base change of rational elliptic surfaces
• 6D SCFTs and Gravity
• General F-theory models with tuned $(\mathrm{SU}(3)\times \mathrm{SU}(2)\times U(1))/{\mathbb{Z}}_6$ symmetry
• Modularity from Monodromy
• 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
• When Rational Sections Become Cyclic: Gauge Enhancement in F-theory via Mordell--Weil Torsion
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines
• Infinitely many 4d N=1 SCFTs with a=c
• Automatic Enhancement in 6D Supergravity and F-theory Models
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Incidence Geometry in a Weyl Chamber I: $G{L}_n$
• On the Standard Model Group in F-theory
• 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
• On finiteness of Type IIB compactifications: Magnetized branes on elliptic Calabi-Yau threefolds
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• On $E_8$ and F-Theory GUTs
• 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
• Extremal 1/2 Calabi-Yau 3-folds and six-dimensional F-theory applications
• 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
• Notes on anomalies, elliptic curves and the BS-D conjecture
• The origin of discrete symmetries in F-theory models
• Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
• Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for gauge groups in four-dimensional F-theory
• $\frac{1}{2}$Calabi-Yau 4-folds and four-dimensional F-theory on Calabi-Yau 4-folds with U(1) factors