The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of non-linear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point half way to the diffusive pole, at frequency ω = − i 2 Dk 2 . We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

Abstract:The planar N = 2 * Super-Yang-Mills (SYM) theory is solved at large 't Hooft coupling using localization on S 4 . The solution permits detailed investigation of the resonance phenomena responsible for quantum phase transitions in infinite volume, and leads to quantitative predictions for the semiclassical string dual of the N = 2 * theory.

The N = 2 * Super-Yang-Mills theory (SYM*) undergoes an infinite sequence of large-N quantum phase transitions. We compute expectation values of Wilson loops in k-symmetric and antisymmetric representations of the SU(N ) gauge group in this theory and show that the same phenomenon that causes the phase transitions at finite coupling leads to a non-analytic dependence of Wilson loops on k/N when the coupling is strictly infinite, thus making the higher-representation Wilson loops ideal holographic probes of the non-trivial phase structure of SYM*.