The Potential for the Phase of the Wilson line at Nonzero Quark Density

TL;DR

This paper investigates how quark contributions affect the phase of the Wilson line at nonzero temperature and chemical potential, revealing conditions for Bose condensation and potential implications for quark matter phases.

Contribution

It provides a detailed calculation of the quark contribution to the Wilson line phase potential at one and two loops, highlighting new effects at nonzero temperature and chemical potential.

Findings

At zero temperature, the effective potential for the Wilson line phase vanishes.

At nonzero temperature, certain phases have free energy equal to bosons.

Quarks can Bose condense at nonzero chemical potential with negative density.

Abstract

The contribution of quarks to the effective potential for the phase of the Wilson line is computed at nonzero temperature and quark chemical potential to one and two loop order. At zero temperature, regardless of the value of the quark chemical potential, the effective potential for the phase of the Wilson line vanishes. At nonzero temperature, for special values of the phase the free energy of quarks equals that of bosons; at nonzero chemical potential, such quarks can ``Bose condense'', albeit with negative density.