Topology (electrical circuits)

Pure mathematics

Mathematics

Mathematical physics

Abelian group

Theoretical physics

Quantum mechanics

Homogeneous space

Medicine

S-duality

Combinatorics

Gauge group

Instanton

Surgery

Gauge theory

Geometry

Symmetry group

Quantum

Relationship between string theory and quantum field theory

Quantum gravity

Physics

String theory

Torsion (gastropod)

Physical review. D/Physical review. D.

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.

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