Complex saddle points in finite-density QCD

TL;DR

This paper explores complex saddle points in finite-density QCD, revealing how symmetry constraints influence the phase structure and lead to oscillatory behaviors in color-charge densities, with implications for understanding confinement.

Contribution

It introduces a symmetry-constrained approach to complex saddle points in finite-density QCD, highlighting the role of complex mass matrices and their impact on phase structure and confinement.

Findings

Polyakov loop and conjugate loop are real but not identical.

Complex mass matrix leads to oscillatory color-charge densities.

Phase structure is sensitive to the confinement modeling.

Abstract

We consider complex saddle points in QCD at finite temperature and density, which are constrained by symmetry under charge and complex conjugations. This approach naturally incorporates color neutrality, and the Polyakov loop and the conjugate loop at the saddle point are real but not identical. Moreover, it can give rise to a complex mass matrix associated with the Polyakov loops, reflecting oscillatory behavior in color-charge densities. This aspect of the phase structure appears to be sensitive to the origin of confinement, as modeled in the effective potential.