Consistency of lattice definitions of U(1) flux in Abelian projected SU(2) gauge theory

TL;DR

This paper redefines flux and currents in lattice U(1) gauge theory to satisfy Maxwell equations exactly, leading to a consistent and improved description of the dual Abrikosov vortex and confining string.

Contribution

It introduces a novel lattice flux and current definition that ensures Maxwell equations are exactly satisfied at finite lattice spacing, refining previous methods.

Findings

Unique flux and current definitions satisfying Maxwell equations

Magnetic current composed of smeared monopoles

Improved understanding of the dual Abrikosov vortex

Abstract

We reexamine the dual Abrikosov vortex under the requirement that the lattice averages of the fields satisfy exact Maxwell equations [ME]. The electric ME accounts for the total flux and the magnetic ME determines the shape of the confining string. This leads to unique and consistent definitions of flux and electric and magnetic currents at finite lattice spacing. The resulting modification of the standard DeGrand-Toussaint construction gives a magnetic current comprised of smeared monopoles.