Implications of imaginary chemical potential for model building of QCD

TL;DR

This paper explores how properties of QCD at imaginary chemical potential, especially the electric holonomy, can inform the development of effective low-energy models by incorporating holonomy effects into coupling constants.

Contribution

It introduces the entanglement vertex to include holonomy effects in effective models and justifies it through derivations in the Nambu--Jona-Lasinio model, addressing model ambiguities.

Findings

Holonomy effects significantly influence thermodynamic quantities.

The entanglement vertex can be derived from effective four-fermi interactions.

Calculations with different $ ext{Z}_3$ sectors help clarify model ambiguities.

Abstract

Properties of QCD at finite imaginary chemical potential are revisited to utilize for the model building of QCD in low energy regimes. For example, the electric holonomy which is closely related to the Polyakov-loop drastically affects thermodynamic quantities beside the Roberge-Weiss transition line. To incorporate several properties at finite imaginary chemical potential, it is important to introduce the holonomy effects to the coupling constant of effective models. This extension is possible by considering the entanglement vertex. We show justifications of the entanglement vertex based on the derivation of the effective four-fermi interaction in the Nambu--Jona-Lasinio model and present its general form with the local approximation. To discuss how to remove model ambiguities in the entanglement vertex, we calculate the chiral condensate with different $\mathbb{Z}_3$ sectors and the dual quark condensate.