A PNJL model in 0+1 Dimensions

TL;DR

This paper formulates a 0+1 dimensional version of the PNJL model, capturing thermodynamic properties and spectral oscillations near the transition temperature, similar to higher dimensions.

Contribution

It introduces a simplified 0+1 dimensional PNJL model that reproduces key thermodynamic behaviors and spectral features of the 3+1 dimensional theory.

Findings

Pressure and susceptibilities resemble 3+1 dimensional results.

Behavior near transition temperature involves lowest Matsubara frequency and Polyakov line.

UV Dirac spectrum exhibits oscillations near transition temperature.

Abstract

We formulate the Polyakov-Nambu-Jona-Lasinio (PNJL) model in 0+1 dimensions. The thermodynamics captured by the partition function yields a bulk pressure, as well as quark susceptibilities versus temperature that are similar to the ones in 3+1 dimensions. Around the transition temperature the behavior in the pressure and quark susceptibilities follows from the interplay between the lowest Matsubara frequency and the Polyakov line. The reduction to the lowest Matsubara frequency yields a matrix Model. In the presence of the Polyakov line the UV part of the Dirac spectrum features oscillations when close to the transition temperature.