We discuss recent results in the study the evolution of strongly coupled field theories in the presence of time dependent couplings using the holographic correspondence. The aim is to understand (i) thermalization and (ii) universal behavior when the coupling crosses a critical point. Our emphasis is on situations where a subset of bulk fields can be treated in a probe approximation. We consider two different setups. In the first, defect conformal field theories are described by probe branes in AdS space-times, and an initial vacuum state evolves due to a time dependent coupling in the probe sector. While a black hole formation is invisible in this approximation, we show that thermalization can nevertheless happen - this is signalled by formation of apparent horizons on the brane worldvolume. In the second setup, we consider a probe bulk scalar field in the background of a AdS black brane. In equilibrium, this system undergoes a critical phase transition at some temperature when the source for the dual operator vanishes. For a time dependent source which goes across this critical point, we show that a zero mode of the bulk field dominates the dynamics and leads to scaling behavior of the order parameter as a function of the rate of change.
展开▼
