Towards a field theory for dynamical transitions between macroscopically synchronised states

Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the fluctuation-dissipation relations as well as the existence of non-static stable states, or phases. Analogously to equilibrium statistical field theories (SFTs), it is crucial to understand the phenomenology of such models constrained by various symmetries. O(N) has been broadly studied as a paradigmatic symmetry group in the context of SFTs, and has also been a topic of emergent interest in the framework of non-equilibrium dynamical phase transitions. In this work we propose an O(2) symmetric model that has a transition between two ordered non-static phases. More concretely, a phase with a stable limit cycle transitions into a phase with two stable limit cycles of different radii through an exceptional point. We explore that transition using various field-theoretical tools and attempt to draw conclusions on some universal features pertaining to transitions between non-static phases.