The ideal hydrodynamic limit and non-Abelian gauge symmetries

Abstract

We show that the ideal fluid local equilibrium limit, defined as the existence of a flow frame which characterises the direction of both a conserved entropy current and conserved charge currents is incompatible with non-Abelian gauge theory if local color charge density is non-zero. Instead, the equation of state becomes dependent on via modes which are roughly equivalent to ghost modes in the hydrodynamic limit. These modes can be physically imagined as a field of “purcell swimmers” whose “arms and legs” are outstretched in Gauge space. Also, vorticity should couple to the Wilson loop via the chromo-electro-magnetic field tensor, which in local equilibrium is not a “force” but instead represents the polarization tensor of the gluons. We show that because of this coupling vorticity also acquires swirling non-hydrodynamic modes. We then argue that these swirling and swimming non-hydrodynamic modes are the manifestation of gauge redundancy within local equilibrium, and speculate on their role in quark-gluon plasma thermalization.