Cosmological anti-deSitter space-times and time-dependent AdS/CFT correspondence

TL;DR

This paper investigates five-dimensional cosmological solutions with negative curvature to explore time-dependent AdS/CFT correspondence, revealing discrepancies due to particle creation and identifying backgrounds that reproduce the conformal anomaly.

Contribution

It introduces new time-dependent cosmological solutions in AdS space and analyzes their implications for the AdS/CFT correspondence, highlighting effects like particle creation.

Findings

Discrepancies with standard AdS/CFT due to time-dependent effects

Identification of backgrounds reproducing the conformal anomaly

Wilson line calculations show Coulomb repulsion in certain backgrounds

Abstract

We study classes of five-dimensional cosmological solutions with negative curvature, which are obtained from static solutions by an exchange of a spatial and temporal coordinate, and in some cases by an analytic continuation. Such solutions provide a suitable laboratory to address the time-dependent AdS/CFT correspondence. For a specific example we address in detail the calculation of the boundary stress-energy and the Wilson line and find disagreement with the standard AdS/CFT correspondence. We trace these discrepancies to the time-dependent effects, such as particle creation, which we further study for specific backgrounds. We also identify specific time-dependent backgrounds that reproduce the correct conformal anomaly. For such backgrounds the calculation of the Wilson line in the adiabatic approximation indicates only a Coulomb repulsion.