No Area Law in QCD

TL;DR

This paper critically examines Wilson's area law in QCD, demonstrating that the observed area law is an artifact and not physically meaningful, especially when considering the conjugate Wilson action in the strong coupling limit.

Contribution

It shows that Wilson's area law in QCD is an artifact and not a physical property, challenging its validity as a confinement indicator.

Findings

Wilson loop expectation value vanishes with conjugate Wilson action in strong coupling

Finite Wilson loop values with Wilson action are artifacts

Area law in QED indicates it is unphysical

Abstract

Wilson's area law in QCD is critically examined. It is shown that the expectation value of the Wilson loop integral $ \exp(\int iA_\mu dx^\mu) $ in the strong coupling limit vanishes when we employ the conjugate Wilson action which has a proper QED action in the continuum limit. The finite value of Wilson loop with the Wilson action is due to the result of the artifact. The fact that his area law is obtained even for QED simply indicates that the area law is unphysical.