Vacuum structure and Casimir scaling in Yang-Mills theories

TL;DR

This paper investigates the vacuum structure of Yang-Mills theories, proposing a domain-based model that predicts Casimir scaling of string tensions, supported by lattice gauge theory evidence and ground-state wave-functional considerations.

Contribution

It introduces a domain structure model of the Yang-Mills vacuum that predicts Casimir scaling, supported by lattice evidence in G(2) gauge theory and ground-state wave-functional insights.

Findings

Evidence for Casimir scaling in G(2) lattice gauge theory

Support for the domain model from ground-state wave-functional

Proportionality of string tensions to quadratic Casimir eigenvalues

Abstract

The vacuum of Yang-Mills theories can be imagined as a magnetically disordered medium with domain structure, with color magnetic flux in each domain quantized in units corresponding to the gauge group center. This model leads to the prediction of Casimir scaling, i.e. the proportionality of string tensions of potentials (at intermediate distances) between color sources from higher-representations to eigenvalues of the quadratic Casimir operator. I present evidence for Casimir scaling in G(2) lattice gauge theory. I also discuss support for some ingredients of the model from the recently conjectured form of the Yang-Mills ground-state wave-functional.