HET Seminar | Renormalization Group in far-from-equilibrium states

We study renormalization group flows in far-from-equilibrium states. The study is made tractable by focusing on states that are spatially homogeneous, time-independent, and scale invariant. Such states, in which mode k has occupation number $n_k = k^{-\gamma}$, are well-known in nonlinear physics (going under the name of wave turbulence). RG flow in such states is qualitatively different than in the vacuum -- a positive $\gamma$ decreases the dimension of an operator, turning marginal interactions into relevant interactions. We compute one loop beta functions. Depending on the sign of the beta function, backreaction may either cause a minor shift of the state in the IR, or completely change the nature of the state. Focusing on nearly marginal interactions, we construct an analog of the epsilon expansion and IR fixed points, with epsilon now set by the scaling of the interaction rather than the spacetime dimension. In the language of RG flow, critical balance scaling -- having applications in fields as varied as astrophysics and ocean waves -- corresponds to the state dynamically adjusting itself along the RG flow until the interaction becomes marginal.