Superuniversality of superdifusion in integrable many-body systems with nonabelian symmetries

I will present a plethora of computational evidence for superuniversality of superdiffusive spin (or, generally, Noether charge) transport in integrable spin chains with arbitrary non-abelian symmetries. The most prominent example is the quantum Heisenberg magnet, while other quantum and classical integrable chains with non-abelian Lie group symmetries are shown to yield identical phenomenology. The two-point functions (e.g. dynamical spin structure factor) at high temperature are shown to be described by Kardar-Parisi-Zhang (KPZ) universality class with dynamical exponent z=3/2. This is remarkable, as KPZ universality in stochastic growth and related processes applies to manifesly non-equilibrium situations, while in the present context of equilibrium spin transport we show that KPZ universality breaks down to diffusive universality when introducing non-equilibrium initial states with a finite magnetization bias which break the non-abelian symmetry. The talk will be concluded by the discussion of the most pressing open theoretical questions.