F-theory on singular spaces

Abstract

We propose a framework for treating F-theory directly, without resolving or deforming its singularities. This allows us to explore new sectors of gauge theories, including exotic bound states such as T-branes, in a global context. We use the mathematical framework known as Eisenbud's matrix factorizations for hypersurface singularities. We display the usefulness of this technique by way of examples, including affine singularities of both conifold and orbifold type, as well as a class of full-fledged compact elliptically fibered Calabi-Yau fourfolds.

35 pages, 4 figures, minor revisions

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• Fluxes in F-theory Compactifications on Genus-One Fibrations
• T-Branes at the Limits of Geometry
• T-branes through 3d mirror symmetry
• Gauge Backgrounds and Zero-Mode Counting in F-Theory
• There and back again: A T-brane's tale
• Towards Exotic Matter and Discrete Non-Abelian Symmetries in F-theory
• SUSY enhancement from T-branes
• De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications
• T-branes, monopoles and S-duality
• Box Graphs and Resolutions II: From Coulomb Phases to Fiber Faces
• T-branes and ${\alpha }^{\prime }$-corrections
• Singular Geometry and Higgs Bundles in String Theory
• Genus zero Gopakumar-Vafa invariants from open strings
• Chiral anomalies on a circle and their cancellation in F-theory
• Compact T-branes
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Higgs Branches of rank-0 5d theories from M-theory on $(A_j,A_l)$ and $(A_k,D_n)$ singularities
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• Fitting fermion masses and mixings in F-theory GUTs
• Holography, Matrix Factorizations and K-stability
• $E_6$ Yukawa couplings in F-theory as D-brane instanton effects
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• Nilpotent Networks and 4D RG Flows
• T-branes and Matrix Models
• $6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
• The two faces of T-branes
• On $E_8$ and F-Theory GUTs
• T-branes and defects
• Higher-dimensional field theories from type II supergravity
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
• Monodromic T-Branes And The $SO(10{)}_{GUT}$
• A note on transition in discrete gauge groups in F-theory
• On the Sen limit squared
• Orientifold limits of singular $F$-theory vacua
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence
• Matrix Factorizations for Local F-Theory Models
• Root bundles: Applications to F-theory Standard Models
• Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification (String Math 2022 Proceedings)
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings