General structure of relativistic vector condensation

We study relativistic massive vector condensation due to a nonzero chemical potential associated with some of the globally conserved charges of the theory. We show that the phase structure is very rich. More specifically, there are three distinct phases depending on the value of one of the zero chemical potential vector self-interaction terms. We also develop a formalism which enables us to investigate the vacuum structure and dispersion relations in the spontaneously broken phase of the theory. We show that, in a certain limit of the couplings and for a large chemical potential, the theory is not stable. This limit, interestingly, corresponds to a gauge-type limit often employed to economically describe the ordinary vector mesons self-interactions in QCD. We finally indicate for which physical systems our analysis is relevant.