$\frac{1}{2}$Calabi-Yau 4-folds and four-dimensional F-theory on Calabi-Yau 4-folds with U(1) factors

Abstract

In this study, four-dimensional $N=1$ F-theory models with multiple U(1) gauge group factors are constructed. A class of rational elliptic 4-folds, which we call as "$\frac{1}{2}$Calabi-Yau 4-folds," is introduced, and we construct the elliptically fibered 4-folds by utilizing them. This yields a novel approach for building families of elliptically fibered Calabi-Yau 4-folds with positive Mordell-Weil ranks. The introduced $\frac{1}{2}$Calabi-Yau 4-folds possess the characteristic property wherein the sum of the ranks of the singularity type and the Mordell-Weil group is always equal to six. This interesting property enables us to construct the elliptically fibered Calabi-Yau 4-folds of various positive Mordell-Weil ranks. From one to six U(1) factors form in four-dimensional F-theory on the resulting Calabi-Yau 4-folds. We also propose the geometric condition on the base 3-fold of the built Calabi-Yau 4-folds that allows four-dimensional F-theory models that have heterotic duals to be distinguished from those that do not.

arXiv comment17 pages. Minor changes and references added

References in corpus (32)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• On the Geometry of the String Landscape and the Swampland
• M Theory, Orientifolds and G-Flux
• M-Theory on Eight-Manifolds
• On Flux Quantization In M-Theory And The Effective Action
• The String Landscape and the Swampland
• Vector Bundles And F Theory
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
• G-flux in F-theory and algebraic cycles
• F-Theory Compactifications with Multiple U(1)-Factors: Constructing Elliptic Fibrations with Rational Sections
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• Moduli in N=1 heterotic/F-theory duality
• Elliptic Fibrations with Rank Three Mordell-Weil Group: F-theory with U(1) x U(1) x U(1) Gauge Symmetry
• The Global Gauge Group Structure of F-theory Compactification with U(1)s
• F-Theory Compactifications with Multiple U(1)-Factors: Addendum
• Swampland Bounds on the Abelian Gauge Sector
• Geometric constraints in dual F-theory and heterotic string compactifications
• 6d SCFTs and U(1) Flavour Symmetries
• 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
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Hypercharge flux in F-theory and the stable Sen limit
• Tall sections from non-minimal transformations
• Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
• G-flux and Spectral Divisors
• Algebraic Cycles and Local Anomalies in F-Theory
• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• Enhancements in F-theory models on moduli spaces of K3 surfaces with $ADE$ rank 17
• The Geometry of SO(3), SO(5), and SO(6) models
• Gauge groups and matter spectra in F-theory compactifications on genus-one fibered Calabi-Yau 4-folds without section - hypersurface and double cover constructions
• F-theory models with 3 to 8 U(1) factors on K3 surfaces