Dual condensates at finite isospin chemical potential

TL;DR

This paper investigates dual condensates as order parameters for center symmetry at finite isospin chemical potential in a QCD model, revealing their temperature dependence and relation to pion condensation.

Contribution

It introduces a dual condensate based on the pion condensate and analyzes its behavior, providing insights into the connection between dual observables and confinement-deconfinement transition.

Findings

The dual condensate's temperature dependence mirrors that of the Polyakov-loop.

Rapid increase of the dual condensate with temperature is linked to pion evaporation.

The dressed Polyakov-loop shows abnormal thermal behavior influenced by pion condensate.

Abstract

The dual observables as order parameters for center symmetry are tested at finite isospin chemical potential $\mu_I$ in a Polyakov-loop enhanced chiral model of QCD with physical quark masses. As a counterpart of the dressed Polyakov-loop, the first Fourier moment of pion condensate is introduced for $\mu_I>{m_\pi}/{2}$ under the temporal twisted boundary conditions for quarks. We demonstrate that this dual condensate exhibits the similar temperature dependence as the conventional Polyakov-loop. We confirm that its rapid increase with $T$ is driven by the evaporating of pion condensation. On the other hand, the dressed Polyakov-loop shows abnormal thermal behavior, which even decreases with $T$ at low temperatures due to the influence of pion condensate. We thus argue that in QCD the critical temperature extracting from a dual observable may have nothing to do with the quark confinement-deconfinement transition if the quark mass is very small.