Polyakov-Nambu-Jona-Lasinio model in 0+1 dimensions

We formulate the Polyakov-Nambu-Jona-Lasinio 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.