Order Parameters for Non-Abelian Gauge Theories

TL;DR

This paper introduces two sets of order parameters for non-Abelian gauge theories, addressing longstanding issues related to quantum fluctuations and gauge fixing, and aiding in understanding their phase structure.

Contribution

It presents a novel formulation of order parameters that directly probe the low energy symmetry group in non-Abelian gauge theories, overcoming previous challenges.

Findings

Two sets of order parameters are proposed.

These operators effectively detect the realization of gauge symmetry.

The approach advances the study of phase diagrams in non-Abelian gauge theories.

Abstract

Owing to subtle issues concerning quantum fluctuations and gauge fixing, a formulation of a general procedure to specify the realization of non-Abelian gauge symmetry has evaded all earlier attempts. In this Letter, we discuss these subtleties and present two sets of order parameters for non-Abelian gauge theories. Such operators directly probe the manifest low energy symmetry group and are crucial for the study of the phase diagram of a non-Abelian gauge theory.