Charge Screening, Large-N, and the Abelian Projection Model of Confinement

TL;DR

This paper examines the abelian projection model of quark confinement, highlighting conflicts with large-N predictions, and presents numerical and theoretical evidence questioning the model's assumptions about charge screening and flux tube interactions.

Contribution

It critically analyzes the abelian projection theory, providing numerical data and strong-coupling arguments that challenge its explanation of confinement mechanisms.

Findings

Perimeter law behavior is due to charge screening, suppressed by 1/N^2 at large scales.

Numerical data shows no significant force difference between abelian charged and neutral adjoint quarks.

Flux tubes attract each other at strong coupling, contrary to vortex behavior in type II superconductors.

Abstract

We point out that the abelian projection theory of quark confinement is in conflict with certain large-N predictions. According to both large-N and lattice strong-coupling arguments, the perimeter law behavior of adjoint Wilson loops at large scales is due to charge-screening, and is suppressed relative to the area term by a factor of $1/N^2$. In the abelian projection theory, however, the perimeter law is due to the fact that $N-1$ out of $N^2-1$ adjoint quark degrees of freedom are (abelian) neutral and unconfined; the suppression factor relative to the area law is thus only $1/N$. We study numerically the behavior of Wilson loops and Polyakov lines with insertions of (abelian) charge projection operators, in maximal abelian gauge. It appears from our data that the forces between abelian charged, and abelian neutral adjoint quarks are not significantly different. We also show via the lattice strong-coupling expansion that, at least at strong couplings, QCD flux tubes attract one another, whereas vortices in type II superconductors repel.