The BF Formalism for QCD and Quark Confinement

TL;DR

This paper develops a BF formalism for QCD that provides a covariant representation of magnetic flux and confirms confinement features like the perimeter and area laws, with a realistic string tension estimate.

Contribution

It introduces a BF-based continuum framework for QCD that explicitly realizes 't Hooft's magnetic flux and confinement mechanisms.

Findings

Perimeter law for magnetic flux operator

Area law for Wilson loop

String tension of correct order of magnitude

Abstract

Using the BF version of pure Yang-Mills, it is possible to find a covariant representation of the 't Hooft magnetic flux operator. In this framework, 't Hooft's pioneering work on confinement finds an explicit realization in the continuum. Employing the Abelian projection gauge we compute the expectation value of the magnetic variable and find the expected perimeter law. We also check the area law behaviour for the Wilson loop average and compute the string tension which turns out to be of the right order of magnitude.