Vacuum structure of pure gauge theories on the lattice

TL;DR

This paper investigates the flux tube structure in pure gauge theories, providing evidence for constant energy density at the flux tube center in SU(2) and confirming the dual London equation in lattice U(1), advancing understanding of quark confinement.

Contribution

It offers new lattice simulation results on flux tube profiles and magnetic monopole currents, elucidating confinement mechanisms in pure gauge theories.

Findings

Energy density at flux tube center approaches a constant with quark separation.

Dual London equation is satisfied in lattice U(1) confinement phase.

Electric fluxoid is quantized in the studied gauge theories.

Abstract

We present results from simulations on two aspects of quark confinement in the pure gauge sector. First is the calculation of the profile of the flux tube connecting a static $q \bar{q}$ pair in $SU(2)$. By using the Michael sum rules as a constraint we give evidence that the energy density at the center of the flux tube goes to a constant as a function of quark separation. Slow variation of the width and energy density is not ruled out. Secondly in the confined phase of lattice $U(1)$ we calculate the curl of the magnetic monopole current and show that the dual London equation is satisfied and that the electric fluxoid is quantized.