Linear sigma model with quarks and Polyakov loop in rotation: phase diagrams, Tolman-Ehrenfest law and mechanical properties

We study the effect of rotation on the confining and chiral properties of QCD using the Polyakov-enhanced linear sigma model coupled to quarks. Working in the homogeneous approximation, we obtain the phase diagram at finite temperature, baryon density and angular frequency, taking into account the causality constraint enforced by the spectral boundary conditions at a cylindrical surface. We explicitly address various limits with respect to system size $R$, angular frequency $\Omega$ and chemical potential $\mu$. We demonstrate that, in this model, the critical temperatures of both the chiral restoration and the deconfinement transitions diminish in response to the increasing rotation, being in contradiction with the first-principle lattice results. We demonstrate that consistency between the thermodynamics of the model and the Tolman-Ehrenfest law is achieved in the limit of large volume. We also compute the mechanical characteristics of the rotating plasma, such as the moment of inertia and the $K_n$ shape coefficients describing the response of the thermodynamic potential with respect to the increase of angular velocity $\Omega$.