Matter From Geometry Without Resolution

Abstract

We utilize the deformation theory of algebraic singularities to study charged matter in compactifications of M-theory, F-theory, and type IIa string theory on elliptically fibered Calabi-Yau manifolds. In F-theory, this description is more physical than that of resolution. We describe how two-cycles can be identified and systematically studied after deformation. For ADE singularities, we realize non-trivial ADE representations as sublattices of Z^N, where N is the multiplicity of the codimension one singularity before deformation. We give a method for the determination of Picard-Lefschetz vanishing cycles in this context and utilize this method for one-parameter smooth deformations of ADE singularities. We give a general map from junctions to weights and demonstrate that Freudenthal's recursion formula applied to junctions correctly reproduces the structure of high-dimensional ADE representations, including the 126 of SO(10) and the 43,758 of E_6. We identify the Weyl group action in some examples, and verify its order in others. We describe the codimension two localization of matter in F-theory in the case of heterotic duality or simple normal crossing and demonstrate the branching of adjoint representations. Finally, we demonstrate geometrically that deformations correctly reproduce the appearance of non-simply-laced algebras induced by monodromy around codimension two singularities, showing the reduction of D_4 to G_2 in an example. A companion mathematical paper will follow.

30 pages + references, appendices. v2: references and two figures added, typos corrected

References in corpus (12)

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Cited by in corpus (45)

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• Machine Learning in the String Landscape
• SU(5) Tops with Multiple U(1)s in F-theory
• T-Branes and Geometry
• 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
• Yukawas and discrete symmetries in F-theory compactifications without section
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• F-theory on singular spaces
• Non-Higgsable clusters for 4D F-theory models
• Calabi-Yau threefolds with large h^{2, 1}
• ${\mathbb{P}}^1$-bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
• F-theory and 2d (0,2) Theories
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• The Landscape of M-theory Compactifications on Seven-Manifolds with $G_2$ Holonomy
• T-Branes, String Junctions, and 6D SCFTs
• Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• Strong Coupling in F-theory and Geometrically Non-Higgsable Seven-branes
• The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
• Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• Exotic matter on singular divisors in F-theory
• Three-Index Symmetric Matter Representations of SU(2) in F-Theory from Non-Tate Form Weierstrass Models
• F-theory Family Unification
• The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications
• Matter in transition
• Anomaly Nucleation Constrains SU(2) Gauge Theories
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• $6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
• On finiteness of Type IIB compactifications: Magnetized branes on elliptic Calabi-Yau threefolds
• GUTs without guts
• Orders of Vanishing and U(1) Charges in F-theory
• Dualities of Deformed $\mathcal{N}=2$ SCFTs from Link Monodromy on D3-brane States
• Anomaly-free Multiple Singularity Enhancement in F-theory
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
• A dessin on the base: a description of mutually non-local 7-branes without using branch cuts
• Non-split singularities and conifold transitions in F-theory
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings