Towards the Standard Model in F-theory

Abstract

This article explores possible embeddings of the Standard Model gauge group and its matter representations into F-theory. To this end we construct elliptic fibrations with gauge group SU(3)xSU(2)xU(1)xU(1) as suitable restrictions of a ${\mathrm{Bl}}_2{\mathbb{P}}^2$-fibration with rank-two Mordell-Weil group. We analyse the five inequivalent toric enhancements to gauge group SU(3)xSU(2) along two independent divisors W_3 and W_2 in the base. For each of the resulting smooth fibrations, the representation spectrum generically consists of a bifundamental (3,2), three types of (1,2) representations and five types of (3,1) representations (plus conjugates), in addition to charged singlet states. The precise spectrum of zero-modes in these representations depends on the 3-form background. We analyse the geometrically realised Yukawa couplings among all these states and find complete agreement with field theoretic expectations based on their U(1) charges. We classify possible identifications of the found representations with the Standard Model field content extended by right-handed neutrinos and extra singlets. The linear combination of the two abelian gauge group factors orthogonal to hypercharge acts as a selection rule which, depending on the specific model, can forbid dangerous dimension-four and -five proton decay operators.

v2,3: typos corrected, references added, minor corrections, Appendix A on symmetries of tops included

References in corpus (20)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Spacetime Instanton Corrections in 4D String Vacua - The Seesaw Mechanism for D-Brane Models
• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• A Mini-Landscape of Exact MSSM Spectra in Heterotic Orbifolds
• Neutrino Majorana Masses from String Theory Instanton Effects
• Lectures on F-theory compactifications and model building
• Stringy Instantons and Quiver Gauge Theories
• Gaugino Condensates and D-terms from D7-branes
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Progress in D-brane model building
• Orientifolds, hypercharge embeddings and the Standard Model
• The N=1 effective action of F-theory compactifications
• Gauge Coupling Unification in F-theory GUT Models
• Non-perturbative Yukawa Couplings from String Instantons
• Toric Construction of Global F-Theory GUTs
• The Importance of Being Rigid: D6-Brane Model Building on T6/Z2xZ6' with Discrete Torsion
• Stringy Instantons and Yukawa Couplings in MSSM-like Orientifold Models
• Grand Unification and Intermediate Scale Supersymmetry
• Axiology
• Anomaly Nucleation Constrains SU(2) Gauge Theories

Cited by in corpus (21)

• Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
• The Global Gauge Group Structure of F-theory Compactification with U(1)s
• 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
• Machine learning Calabi-Yau metrics
• F-theory and 2d (0,2) Theories
• A Quadrillion Standard Models from F-theory
• G4-Flux and Standard Model Vacua in F-theory
• Flavour mixings in flux compactifications
• An F-theory Realization of the Chiral MSSM with ${\mathbb{Z}}_2$-Parity
• Mordell-Weil Torsion in the Mirror of Multi-Sections
• Tate's Algorithm for F-theory GUTs with two U(1)s
• The Standard Model from String Theory: What Have We Learned?
• Statistics of Flux Vacua for Particle Physics
• The Toric SO(10) F-Theory Landscape
• D6-Brane Model Building on Z(2)xZ(6): MSSM-like and Left-Right Symmetric Models
• 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
• Generic construction of the Standard Model gauge group and matter representations in F-theory
• Constraints on Standard Model Constructions in F-theory
• Yukawa Hierarchies in Global F-theory Models