 One-form symmetry

A one-form symmetry is a global symmetry in field theory whose charged observables are line operators. In $d$ spacetime dimensions, its symmetry operators lie on closed manifolds of dimension $d-2$, so their codimension is two. This differs from the codimension-one symmetry operators of an ordinary zero-form global symmetry.

A symmetry surface acts on a charged line through their linking. It can be deformed without changing a correlation function as long as it does not cross charged insertions; crossing changes the function by the relevant symmetry action. In four spacetime dimensions these generators are surfaces, while the charged observables remain lines. This language organizes constraints on gauge theories and distinguishes global symmetry data from a redundant local gauge description. ^[ref]