Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations

Abstract

We realize higher-form symmetries in F-theory compactifications on non-compact elliptically fibered Calabi-Yau manifolds. Central to this endeavour is the topology of the boundary of the non-compact elliptic fibration, as well as the explicit construction of relative 2-cycles in terms of Lefschetz thimbles. We apply the analysis to a variety of elliptic fibrations, including geometries where the discriminant of the elliptic fibration intersects the boundary. We provide a concrete realization of the 1-form symmetry group by constructing the associated charged line operator from the elliptic fibration. As an application we compute the symmetry topological field theories in the case of elliptic three-folds, which correspond to mixed anomalies in 5d and 6d theories.

57 pages, tikz figures, added clarifications

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Cited by in corpus (12)

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• The Branes Behind Generalized Symmetry Operators
• Lecture Notes on Generalized Symmetries and Applications
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• 2-Group Symmetries and M-Theory
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• Higher Form Symmetries TFT in 6d
• Anomalies of Generalized Symmetries from Solitonic Defects
• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Disconnected 0-Form and 2-Group Symmetries
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds