Surface Observables, 2-Knot Invariants, and Nonabelian Electric Fluxes

Abstract

Abstract This work introduces a surface observable for nonabelian four-dimensional BF theory with a cosmological term. The surface observable yields new 2-knot invariants that may extend beyond known examples such as the Alexander invariant. By BV pushforward, the surface observable induces an electric observable in nonabelian Yang–Mills theory, offering a concrete realization of ’t Hooft operators. An application to self-dual Yang–Mills theory is also discussed.