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

TL;DR

This paper introduces a new surface observable in nonabelian 4D $BF$ theory that produces novel $2$-knot invariants and connects to electric fluxes in Yang-Mills theory, with implications for topological and gauge theories.

Contribution

It presents a novel surface observable in nonabelian 4D $BF$ theory that generates new $2$-knot invariants and relates to electric fluxes in Yang-Mills theory.

Findings

New $2$-knot invariants beyond Alexander invariant

Surface observable induces 't Hooft operators in Yang-Mills

Application to self-dual Yang-Mills theory

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.