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 saddlepoint 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 non-analyticity 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.

Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in 2, 3, and 4 dimensions to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volumeindependent for small volumes, but slows for larger volumes. In this setting, the UV thermalizes first.

This paper describes the background field equations for strings in T-duality symmetric formalisms in which the dimension of target space is doubled and the sigma model supplemented with constraints. These are calculated by demanding the vanishing of the beta-functional of the sigma model couplings in the doubled target space. We demonstrate the equivalence with the background field equations of the standard string sigma model.