Effective field theory near and far from equilibrium

In this talk I will discuss effective field theories for two classes of non-equilibrium systems, one far and one near equilibrium. The backbone of the approach is the Schwinger-Keldysh formalism, which is the natural starting point for doing field theory in non-equilibrium situations. In the first part of the talk I will present an effective response for topological driven (Floquet) systems, which are inherently far from equilibrium. As an example, I will discuss a chiral Floquet drive coupled to a background $U(1)$ field, which gives rise to a theta term in the response action, and show that this is independent of smooth deformations of the underlying system. In the second part, I will discuss an ongoing project using effective field theories for hydrodynamics. I will show that chiral diffusion for interacting systems in 1+1 dimensions, which may be relevant to edge transport in quantum Hall systems, has an infrared instability. I will then discuss the fate of this instability.