Quark number holonomy and confinement-deconfinement transition

TL;DR

This paper introduces the quark number holonomy, a topological quantity based on the quark number susceptibility, to characterize the confinement-deconfinement transition in QCD, providing a new perspective on phase transition analysis.

Contribution

The paper proposes the quark number holonomy as a novel topological order parameter for the confinement-deconfinement transition in QCD.

Findings

Quark number holonomy is defined as an integral of susceptibility over imaginary chemical potential.

Expected behaviors of the holonomy at finite temperature are discussed.

Asymptotic behaviors of the holonomy are demonstrated.

Abstract

We propose a new quantity which describes the confinement-deconfinement transition based on topological properties of QCD. The quantity which we call the quark number holonomy is defined as the integral of the quark number susceptibility along the closed loop of $\theta$ where $\theta$ is the dimensionless imaginary chemical potential. Expected behavior of the quark number holonomy at finite temperature is discussed and its asymptotic behaviors are shown.