Quantum models with gauge fields typically include observables called Wilson operators and 't Hooft operators. These operators are nominally localized on lower-dimensional submanifolds of spacetime, in the same sense that scalar field operators are nominally localized at individual points in spacetime. Some Wilson operators are localized on closed curves C, and some are localized on 2-dimensional submanifolds that may have a boundary inside spacetime. Some 't Hooft operators are localized on closed submanifolds Γ with codimension 3 in spacetime, and some are localized on submanifolds with codimension 2 that may have a boundary inside spacetime. Other articles introduce these operators in detail. This article summarizes the pattern.
