SU($N_c$) confinement and color $N_c$-ality

TL;DR

This paper explores the relationship between confinement, quark screening, and color N_c-ality in SU(N_c) gauge theories, extending previous results and proposing a thermodynamic interpretation of these phenomena.

Contribution

It generalizes earlier findings to SU(N_c) groups, considers various color representations, and offers a thermodynamic rationale linking confinement and N_c-ality without Euclidean methods.

Findings

Net quark number differs in confined and deconfined phases.

Color N_c-ality acts as a proxy for center symmetry.

Proposed thermodynamic argument for confinement phenomena.

Abstract

In a recent work, we have argued that the net quark number gained by a bath of quarks and gluons upon bringing an external static quark probe, while being equal to $1$ in the high temperature, deconfined phase, is equal to $0$ or $3$ in the low temperature, confined phase, depending on the value of the quark chemical potential. This establishes a clear-cut connection between the confinement of a medium as probed by order parameters such as the Polyakov loop, and the ability of that same medium to screen the quark probe into states with the same net quark content as mesons or baryons. In this work, we extend these findings to the SU($N_c$) color group, consider color probes in various (fundamental and non-fundamental) representations, and conjecture a rationale of how these results could be recovered from a purely thermodynamic argument that shortcuts the use of the Euclidean functional framework, while emphasizing the role of color $N_c$-ality as a proxy for center symmetry within the Minkowskian framework.