Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality

TL;DR

This paper investigates higher-form symmetries and their anomalies in M- and F-theory compactifications, revealing geometric and topological structures that encode gauge group properties and anomaly phenomena in various dimensions.

Contribution

It establishes a geometric framework linking higher-form symmetries, Mordell--Weil torsion, and string junctions, and analyzes anomalies arising from torsional fluxes in F-/M-theory compactifications.

Findings

Higher-form symmetries are characterized by boundary topology.

Torsional G_4-fluxes encode background gauge fields for 1-form symmetries.

Anomalies are identified as fractionalized instanton numbers in compactifications.

Abstract

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 $G_4$-fluxes, which encode background gauge fields of center 1-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as 't Hooft anomalies involving the 1-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.