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 electric and magnetic field operators are nominally localized at individual points in spacetime. This article introduces a type of 't Hooft operator that is nominally localized on a (d-3)-dimensional closed submanifold Γ in d-dimensional spacetime, treating spacetime as discrete to make the math clear. The gauged group G can be any compact connected Lie group. The operators are constructed by modifying the action in a tubular neighborhood of Γ so that the path integral is dominated by configurations of the gauge field the approach a prescribed GNO configuration near Γ. The GNO configuration is based on a specially chosen connection for a principal G-bundle. Article 49708 explains how to construct the G-bundle and the connection and explains the reason for the name GNO.
