Higher Form Symmetries and M-theory

Understand

We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory.

• The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields.
• We analyze the example of 4d $\mathcal{N}=1$ SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines.
• We extend this analysis to the case of 7d $\mathcal{N}=1$ SYM theory, where we recover it from a mixed 't Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group.