Color Screening, Casimir Scaling, and Domain Structure in G(2) and SU(N) Gauge Theories

TL;DR

This paper explores how vacuum domain structures and magnetic flux quantization in non-abelian gauge theories explain Casimir scaling of string tensions, with numerical results for G(2) gauge group and a critique of subgroup projections.

Contribution

It introduces a domain structure model linking magnetic flux quantization to Casimir scaling and provides numerical evidence for G(2) gauge theory, including a critical view on subgroup projections.

Findings

Casimir scaling arises from magnetic flux variations within domains

G(2) gauge group exhibits a single vacuum domain type

Numerical results support the domain structure model

Abstract

We argue that screening of higher-representation color charges by gluons implies a domain structure in the vacuum state of non-abelian gauge theories, with the color magnetic flux in each domain quantized in units corresponding to the gauge group center. Casimir scaling of string tensions at intermediate distances results from random spatial variations in the color magnetic flux within each domain. The exceptional G(2) gauge group is an example rather than an exception to this picture, although for G(2) there is only one type of vacuum domain, corresponding to the single element of the gauge group center. We present some numerical results for G(2) intermediate string tensions and Polyakov lines, as well as results for certain gauge-dependent projected quantities. In this context, we discuss critically the idea of projecting link variables to a subgroup of the gauge group. It is argued that such projections are useful only when the representation-dependence of the string tension, at some distance scale, is given by the representation of the subgroup.