Confinement and Chiral Phase Transitions: The Role of Polyakov Loop Kinetics Terms

TL;DR

This paper derives the kinetic term of the Polyakov loop from first principles and shows its significant impact on gravitational wave predictions from confinement transitions, while having little effect on chiral transition dynamics.

Contribution

First derivation of the Polyakov loop kinetic term from fundamental theory and analysis of its effects on phase transition predictions and gravitational wave signals.

Findings

Kinetic term modifies GW spectrum predictions by 1-2 orders of magnitude.

Polyakov-loop kinetic term critically influences confinement transition GWs.

Chiral transition dynamics are largely unaffected by the kinetic term.

Abstract

We studied a crucial but often oversimplified ingredient in predicting gravitational-wave signals from QCD-type phase transitions: the kinetic term of the Polyakov loop. For the first time, we derive this term from first principles in finite-temperature pure SU(3) Yang-Mills theory, incorporating a field-dependent renormalization factor--a calculation we also extend to theories with more colors. Employing this derived kinetic term alongside three commonly-used effective potentials (the Haar-measure, polynomial, and quasi-particle models), we demonstrate that it substantially modifies the predicted GW energy spectrum from confinement transitions by 1-2 orders of magnitude. Based on this, we provide the first complete analysis of the chiral transition within the Polyakov-Nambu-Jona-Lasinio (PNJL) framework, described by the quark condensate. Our results reveal a clear dichotomy: while the Polyakov-loop kinetic term critically shapes GWs from confinement transitions, it has a negligible impact on the dynamics of the chiral transition, which is dominated by fermion condensation effects.