Large Loops of Magnetic Current and Confinement in Four Dimensional $U(1)$ Lattice Gauge Theory

TL;DR

This paper demonstrates that in four-dimensional U(1) lattice gauge theory, the long-range heavy quark potential and confinement are primarily due to large magnetic current loops that wrap around the lattice, identified through monopole analysis.

Contribution

It introduces a method to compute the string tension from large magnetic current loops, linking monopole dynamics to confinement in lattice gauge theory.

Findings

Wrapping magnetic loops only appear in the confined phase.

The long-range potential is determined by large, wrapping magnetic loops.

The magnetic current analysis effectively captures the confinement mechanism.

Abstract

We calculate the heavy quark potential from the magnetic current due to monopoles in four dimensional $U(1)$ lattice gauge theory. The magnetic current is found from link angle configurations using the DeGrand-Toussaint identification method. The link angle configurations are generated in a cosine action simulation on a $24^4$ lattice. The magnetic current is resolved into large loops which wrap around the lattice and simple loops which do not. Wrapping loops are found only in the confined phase. It is shown that the long range part of the heavy quark potential, in particular the string tension, can be calculated solely from the large, wrapping loops of magnetic current.