$6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces

Abstract

In this paper we study the 6d localized charged matter spectrum of F-theory directly on a singular elliptic Calabi-Yau 3-fold, i.e. without smoothing via resolution or deformation of the entire fibration. Given only the base surface, discriminant locus, and the $SL(2,\mathbb{Z})$ local system, we propose a general prescription for determining the charged matter spectrum localized at intersections of seven-branes, using the technology of string junctions. More precisely, at each codimension-$2$ collision of seven-branes, we determine the local seven-brane content and compute the number of massless string junctions modulo the action of the $SL(2,\mathbb{Z})$ monodromy. We find agreement with the predicted results from $6$d anomaly cancellation in all cases considered. Examples include a generic Weierstrass model with arbitrary Kodaira fiber intersecting an $I_1$, as well as cases with jointly charged matter localized at intersections of non-abelian seven-branes.

References in corpus (27)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Geometric Singularities and Enhanced Gauge Symmetries
• Matter From Geometry
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's
• Matter and singularities
• Geometric Engineering of N=1 Quantum Field Theories
• Tate's algorithm and F-theory
• Exceptional groups from open strings
• String Junctions for Arbitrary Lie Algebra Representations
• Global F-theory Models: Instantons and Gauge Dynamics
• Box Graphs and Singular Fibers
• The Tate Form on Steroids: Resolution and Higher Codimension Fibers
• On Algorithmic Universality in F-theory Compactifications
• Terminal Singularities, Milnor Numbers, and Matter in F-theory
• Constraints on the BPS Spectrum of N = 2, D = 4 Theories with A-D-E Flavor Symmetry
• F-theory on singular spaces
• Matter From Geometry Without Resolution
• A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• Three Looks at Instantons in F-theory -- New Insights from Anomaly Inflow, String Junctions and Heterotic Duality
• Strong Coupling in F-theory and Geometrically Non-Higgsable Seven-branes
• Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• Normal Factorization in $SL(2,Z)$ and the Confluence of Singular Fibers in Elliptic Fibrations
• Dualities of Deformed $\mathcal{N}=2$ SCFTs from Link Monodromy on D3-brane States

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