PNJL model for adjoint fermions

TL;DR

This paper develops a PNJL model for adjoint fermions in gauge theories, combining perturbative and chiral symmetry breaking effects to analyze phase structure and confinement properties at small circle circumference.

Contribution

It introduces a combined PNJL framework for adjoint QCD that incorporates both perturbative effects and chiral symmetry breaking to study phase transitions.

Findings

The model predicts a rich phase structure with multiple confined phases.

Results align with lattice simulations showing no direct link between small and large L confinement.

Small and large L confined phases are connected via an extended field theory model.

Abstract

Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on R^3 X S^1 can lead to a restoration of center symmetry and confinement for sufficiently small circumference L of S^1. At small L, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop P in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small L. In order for the fermionic effects to dominate gauge field effects in the effective potential, the fermion mass must be sufficiently small. This indicates that chiral symmetry breaking effects are potentially important. We develop a Polyakov-Nambu-Jona Lasinio (PNJL) model which combines the known perturbative behavior of adjoint QCD models at small L with chiral symmetry breaking effects to produce an effective potential for the Polyakov loop P and the chiral order parameter psi-bar psi. A rich phase structure emerges from the effective potential. Our results are consistent with the recent lattice simulations of Cossu and D'Elia, which found no evidence for a direct connection between the small-L and large-L confining regions. Nevertheless, the two confined regions are connected indirectly if an extended field theory model with an irrelevant four-fermion interaction is considered. Thus the small-L and large-L regions are part of a single confined phase.