Anomalous diffusion in nonlinear sigma models

Recent studies of integrable systems that are invariant under a continuous nonabelian global symmetry have shown anomalous finite-temperature transport with dynamical exponent z=3/2. The origin of this superdiffusive behavior is still unclear, despite the fact that a self-consistent framework based on the spreading of long-lived giant quasiparticles dressed by thermal fluctuations has been put forward. In this work, we study the fate of superdiffusive transport in the paradigmatic O(N) nonlinear sigma model using a combination of field theoretic methods and the toolbox of integrability.