Abstract
In the first part of the paper, we discuss different versions of the AdS/CFT dictionary out of equilibrium. We show that the Skenderis - van Rees prescription and the "extrapolate" dictionary are equivalent at the level of "in-in" two point functions of free scalar fields in arbitrary asymptotically AdS spacetimes. In the second part of the paper, we calculate two point correlation functions in dynamical spacetimes using the "extrapolate" dictionary. These calculations are performed for conformally coupled scalar fields in examples of spacetimes undergoing gravitational collapse, the AdS$_2$-Vaidya spacetime and the AdS$_3$-Vaidya spacetime, which allow us to address the problem of thermalization following a quench in the boundary field theory. The computation of the correlators is formulated as an initial value problem in the bulk spacetime. Finally, we compare our results for AdS$_3$-Vaidya to results in the previous literature obtained using the geodesic approximation and we find qualitative agreement.
Highlights
The AdS/CFT duality relates the dynamics of strongly coupled non-equilibirium quantum field theory to semiclassical gravitational dynamics [1, 2]
We show that the Skenderis-van Rees prescription and the “extrapolate” dictionary are equivalent at the level of “in-in” two point functions of free scalar fields in arbitrary asymptotically AdS spacetimes
In the second part of the paper, we calculate two point correlation functions in dynamical spacetimes using the “extrapolate” dictionary. These calculations are performed for conformally coupled scalar fields in examples of spacetimes undergoing gravitational collapse, the AdS2-Vaidya spacetime and the AdS3-Vaidya spacetime, which allow us to address the problem of thermalization following a quench in the boundary field theory
Summary
The AdS/CFT duality relates the dynamics of strongly coupled non-equilibirium quantum field theory to semiclassical gravitational dynamics [1, 2]. In the first part of this paper, we will show that the “extrapolate” dictionary, when generalized to real time (in an obvious way), is equivalent to the SvR dictionary, for “in-in” two point correlators of a free scalar field in an arbitrary asymptotically AdS spacetime. We will demonstrate this by directly constructing a solution to the SvR equations of motion in the glued spacetime and show that this solution is related to a boundary limit of the bulk to bulk two point function.
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