The dual quark condensate in local and nonlocal NJL models: an order parameter for deconfinement?

TL;DR

This paper investigates the dual quark condensate in NJL models and finds that its rise is linked to chiral symmetry restoration, not confinement, questioning its role as an order parameter for deconfinement.

Contribution

The study demonstrates that the dual quark condensate's behavior in NJL models is driven by chiral transition, not confinement, challenging its use as a deconfinement order parameter.

Findings

The dual quark condensate rises at the chiral transition in NJL models.

No qualitative difference in condensate behavior between confining and non-confining models.

The condensate should not be used as an order parameter for confinement without center symmetry relation.

Abstract

We study the beahviour of the dual quark condensate $\Sigma_1$ in the Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum chromodynamics $\Sigma_1$ can be realted to the breaking of the center symmetry and is therefore an (approximate) order parameter of confinement. The deconfinement transition is then signaled by a strong rise of $\Sigma_1$ as a function of temperature. However, a similar behaviour is also seen in the NJL model, which is known to have no confinement. Indeed, it was shown that in this model the rise of $\Sigma_1$ is triggered by the chiral phase transition. In order to shed more light on this issue, we calculate $\Sigma_1$ for several variants of the NJL model, some of which have been suggested to be confining. Switching between "confining" and "non-confining" models and parametrizations we find no qualitative difference in the behaviour of $\Sigma_1$, namely, it always rises in the region of the chiral phase transition. We conclude that without having established a relation to the center symmetry in a given model, $\Sigma_1$ should not blindly be regarded as an order parameter of confinement.