Hydrodynamic Tails in CFT and the Large Dimension Expansion

The late time physics of interacting Quantum Field Theories at finite 
temperature is controlled by hydrodynamics. For CFTs this implies that 
heavy operators -- which are generically expected to create thermal 
states -- can be studied semi-classically. I will show that hydrodynamic 
loops universally fix the OPE coefficients C_{HH'L}, on average, of all 
neutral light operators with two non-identical heavy ones, as a function 
of the scaling dimension and spin of the operators. These methods can be 
straightforwardly extended to CFTs with global symmetries, and 
generalize recent EFT results on large charge operators away from the 
case of minimal dimension at fixed charge.