First evidence for Casimir scaling in G(2) lattice gauge theory

TL;DR

This study provides the first numerical evidence of Casimir scaling in G(2) lattice gauge theory, showing that string tensions in different representations scale proportionally to their Casimir operators.

Contribution

It demonstrates that Casimir scaling occurs in G(2) gauge theory, supporting models of the vacuum with domain structures and magnetic flux quantization.

Findings

Potentials are linearly rising at intermediate distances.

String tensions exhibit approximate Casimir scaling.

Results align with vacuum domain structure models.

Abstract

Potentials between static quarks and antiquarks from a few lowest representations were evaluated in numerical simulations of 4-dimensional pure G$_2$ lattice gauge theory at various couplings. The obtained potentials are linearly rising at intermediate distances and their string tensions exhibit (approximate) Casimir scaling. This result is in accordance with a model of the vacuum of non-Abelian gauge theories with a domain structure, in which the (color) magnetic flux randomly fluctuates within a domain, but the total flux in each domain is quantized in units of the gauge group center.