ADJOINT "QUARK" COLOR FIELDS IN FOUR-DIMENSIONAL LATTICE GAUGE THEORY: VACUUM SCREENING AND PENETRATION

TL;DR

This study investigates the behavior of adjoint and fundamental quark color fields in four-dimensional lattice gauge theory, revealing vacuum screening effects and similarities in flux-tube structures that suggest a dual superconductor vacuum model.

Contribution

It provides the first detailed analysis of adjoint quark fields and flux-tube properties in 4D lattice gauge theory, highlighting vacuum screening and field ratio behaviors.

Findings

Adjoint quarks exhibit vacuum screening effects.

The ratio of color-electric fields approaches Casimir ratios near quarks.

Flux-tube cross-sections are similar for different representations.

Abstract

The fields generated by ``quarks'' in the adjoint representation of SU(2) color are analyzed in the scaling region of the four-dimensional lattice theory. Evidence of vacuum screening of adjoint quarks is obtained from a comparison of quark-antiquark ($Q \bar Q$) flux-tubes for quarks in the adjoint (``isospin'' $j=1$) and fundamental ($j=1/2$) representations. The component ${\cal E}_j$ of the color-electric field strength in the direction parallel to the $Q \bar Q$ axis is calculated. Near the quarks the ratio of fields ${\cal E}_{j=1} / {\cal E}_{j=1/2}$ approaches the value 8/3, which is equal to the ratio of SU(2) Casimirs. In between the quarks, the ratio falls well below 8/3 at large $R$. ${\cal E}_j$ also falls off rapidly as a function of distance $x_\perp$ perpendicular to the $Q \bar Q$ axis. However, the ratio ${\cal E}_{j=1} / {\cal E}_{j=1/2}$ depends very weakly on $x_\perp$. The flux-tubes in the two representations thus appear to have very similar cross-sections. This result could imply that the QCD vacuum is dual to a type I superconductor.