Vortex waistlines and long range fluctuations

TL;DR

This paper investigates how vortex fluctuations of a certain thickness produce a linear potential in gauge theories, revealing that only large-scale vortex fluctuations are responsible, and introduces an effective Z(N) gauge theory to describe these long-range effects.

Contribution

It demonstrates that vortex fluctuations of the order of the loop size are necessary for a linear potential and develops an effective strongly coupled Z(N) gauge theory for these fluctuations.

Findings

Vortex fluctuations of the order of the loop size produce a linear potential.

An effective strongly coupled Z(N) gauge theory describes long-range vortex fluctuations.

Dynamical fermions in this medium exhibit chiral symmetry breaking.

Abstract

We examine the manner in which a linear potential results from fluctuations due to vortices linked with the Wilson loop. Our discussion is based on exact relations and inequalities between the Wilson loop and the vortex and electric flux order parameters. We show that, contrary to the customary naive picture, only vortex fluctuations of thickness of the order of the spatial linear size of the loop are capable of producing a strictly linear potential. An effective theory of these long range fluctuations emerges naturally in the form of a strongly coupled Z(N) lattice gauge theory. We also point out that dynamical fermions introduced in this medium undergo chiral symmetry breaking.