Higher-form and (non-)St\"uckelberg symmetries in non-equilibrium systems

We investigate the role of higher-form symmetries in non-equilibrium systems from the perspective of effective actions defined on the Schwinger-Keldysh contour. To aid our investigation, we extend the coset construction to account for $p$-form symmetries at zero and finite temperature. Additionally we investigate how, out of equilibrium, symmetries of the action need not lead to meaningful conserved currents at the level of the equations of motion. For reasons that will become apparent, we term symmetries with conserved currents St\"uckelberg symmetries and those without meaningful conserved currents non-St\"uckelberg symmetries (NSS). Ordinarily any action constructed exclusively from building-blocks furnished by the coset construction will have St\"uckelberg symmetries associated with each symmetry generator. To expand the set of systems describable by the coset construction, we devise a method by which NSS generators can be included as well. While 0-form NSS are quite common in non-equilibrium effective actions, the introduction of $p$-form NSS is novel. We use these $p$-form NSS to investigate spontaneous symmetry breaking of $p$-form symmetries. We find that in non-equilibrium systems, whether or not a symmetry appears spontaneously broken can depend on the time-scale over which the system is observed. Finally, using our new coset construction, we formulate actions for a number of systems including chemically reacting fluids, Yang-Mills theory, Chern-Simons theory, magnetohydrodynamic systems, and dual superfluid and solid theories.