Non-equilibrium scalar two point functions in AdS/CFT

TL;DR

This paper compares different AdS/CFT dictionaries for out-of-equilibrium two-point functions and computes correlators in dynamical spacetimes to study thermalization after a quench.

Contribution

It demonstrates the equivalence of two AdS/CFT prescriptions for free scalar fields and calculates two-point functions in collapsing spacetimes using the extrapolate dictionary.

Findings

Equivalence of Skenderis - van Rees and extrapolate dictionaries for in-in correlators

Computed correlators in AdS-Vaidya spacetimes during gravitational collapse

Qualitative agreement with previous geodesic approximation results

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.