The Global Gauge Group Structure of F-theory Compactification with U(1)s

Abstract

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell--Weil generators. This results in constraints on the U(1) charges of non-abelian matter consistent with observations made throughout the literature. In particular, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU(3)xSU(2)xU(1)]/Z6. Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an SU(2)xU(1) gauge theory can either unhiggs into an SU(2)xSU(2) or an SU(3)xSU(2) theory. We also study implications of the charge constraints as a criterion for the F-theory 'swampland'.

37 pages; v2: improved derivation of global group structure in section 2, extended discussion on the 'swampland' conjecture in section 5, references added, v2 accepted for publication in JHEP; v3: typos corrected

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• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• Generic matter representations in 6D supergravity theories
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• Discrete gauge groups in certain F-theory models in six dimensions
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
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• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
• Modular Curves and Mordell-Weil Torsion in F-theory
• 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
• Automatic Enhancement in 6D Supergravity and F-theory Models
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• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
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• Constraints on Standard Model Constructions in F-theory
• Geometric Approach to 3D Interfaces at Strong Coupling
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• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• $\frac{1}{2}$ Calabi-Yau 3-folds, Calabi-Yau 3-folds as double covers, and F-theory with U(1)s
• Orders of Vanishing and U(1) Charges in F-theory
• On the Gauge Group Topology of 8d CHL Vacua
• Types of gauge groups in six-dimensional F-theory on double covers of rational elliptic 3-folds
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• Extremal 1/2 Calabi-Yau 3-folds and six-dimensional F-theory applications
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• $\frac{1}{2}$Calabi-Yau 4-folds and four-dimensional F-theory on Calabi-Yau 4-folds with U(1) factors
• Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for gauge groups in four-dimensional F-theory
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings