Using the AdS/CFT correspondence, we probe the scale dependence of thermalization in strongly coupled field theories following a sudden injection of energy via calculations of two-point functions, Wilson loops, and entanglement entropy in $d=2$, 3, 4. In the saddle-point approximation these probes are computed in AdS space in terms of invariant geometric objects—geodesics, minimal surfaces, and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent nonanalyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.

• Received 7 April 2011

DOI:https://doi.org/10.1103/PhysRevD.84.026010