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

Max Hubner, David R. Morrison, Sakura Schafer-Nameki, Yi-Nan Wang

SciPost Phys. 13, 030 (2022) · published 19 August 2022


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.

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