Thermalisation of Wightman Two-Point Functions in AdS/CFT

At first sight, non-local and local probes in holographic models of thermalisation appear to reach their equilibrium values on very different time scales. As an example of non-local probes, we study the evolution of Wightman two-point functions in far-from equilibrium states via the AdS/CFT correspondence. Explicitly, we look at the example of homogeneous quenches in 2d CFTs dual to AdS-Vaidya spacetime. We show that the Wightman two-point functions, after being Fourier transformed to momentum space, decay towards their thermal values with a rate set by the quasinormal modes of the final state black hole spacetime. The quasinormal modes also set the thermalisation time scale of local probes. Generalising our results via a heuristic argument therefore suggests a unified picture of thermalisation times of one- and two-point functions.