Effective field theories of nonlinear fluctuating hydrodynamics in one dimension

Anomalous transport is ubiquitous in one spatial dimension, dating back to the famous Fermi-Pasta-Ulam-Tsingou chain, first discussed in the 50s. Still, to this day, a general approach to describe such behavior in systems with a finite number of charges is not developed. In the past decade, the now celebrated program of nonlinear fluctuating theories was re-introduced, which, along with the development of mode-coupling theory, allowed for predictions on dynamical universality classes. I will discuss the precise consistent application of such a framework for a top-down description of transport as an order-by-order correlator matching procedure, highlighting a few inconsistencies previously not described (arXiv:2607.22527).