F-theory and 2d (0,2) Theories

Abstract

F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.

124 pages, 5 figures, v2: ref added, v3: typos corrected, discussion of interactions extended, v4: updated section 12, v5: typos corrected and refs added

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• Terminal Singularities, Milnor Numbers, and Matter in F-theory
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• UV Completions for Non-Critical Strings
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
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• Orbifold Reduction and 2d (0,2) Gauge Theories
• Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models
• AdS-phobia, the WGC, the Standard Model and Supersymmetry
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• B-branes and supersymmetric quivers in 2d
• $3d$ Printing of $2d$ $\mathcal{N}=(0,2)$ Gauge Theories
• Green-Schwarz Automorphisms and 6D SCFTs
• The Gravitational Sector of 2d (0,2) F-theory Vacua
• Holomorphic field theories and Calabi--Yau algebras
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• A proposal for (0,2) mirrors of toric varieties
• 2d $\mathcal{N}=(0,1)$ Gauge Theories and Spin(7) Orientifolds
• F-theory models with 3 to 8 U(1) factors on K3 surfaces
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• More Toda-like (0,2) mirrors
• From N=2 in four dimensions to (0,2) in two dimensions
• Constructing and Machine Learning Calabi-Yau Five-folds
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• A note on transition in discrete gauge groups in F-theory
• Tetrahedron duality
• Symmetry TFTs from String Theory
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