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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. [ABSTRACT FROM AUTHOR]

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ΛM, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all U(1) factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial π1(G) ≡ Z for the non-Abelian gauge group G as having gauged a Z 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing Z for all 8D CHL vacua with rank (G) = 10. Since our method applies also to T² compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a "parent" heterotic model. [ABSTRACT FROM AUTHOR]