Higher-form symmetries and their anomalies in M-/F-theory duality

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell-Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern-Simons term in the presence of torsional boundary G4-fluxes, which encode background gauge fields of center one-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as 't Hooft anomalies involving the one-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to 8d/7d and 6d/5d.

Automated summary

This study explores higher-form symmetries of M- and F-theory compactified on elliptic fibrations, finding that these symmetries are equivalent to known characterizations of the gauge group topology in F-theory; further investigation into dimensional reductions of the 11d Chern-Simons term led to contributions that can be interpreted as 't Hooft anomalies.