Lorentzian AdS, Wormholes and Holography

Abstract

We investigate the structure of two point functions for the QFT dual to an asymptotically Lorentzian AdS-wormhole. The bulk geometry is a solution of 5-dimensional second order Einstein Gauss Bonnet gravity and causally connects two asymptotically AdS space times. We revisit the GKPW prescription for computing two-point correlation functions for dual QFT operators O in Lorentzian signature and we propose to express the bulk fields in terms of the independent boundary values phi_0^\pm at each of the two asymptotic AdS regions, along the way we exhibit how the ambiguity of normalizable modes in the bulk, related to initial and final states, show up in the computations. The independent boundary values are interpreted as sources for dual operators O^\pm and we argue that, apart from the possibility of entanglement, there exists a coupling between the degrees of freedom leaving at each boundary. The AdS_(1+1) geometry is also discussed in view of its similar boundary structure. Based on the analysis, we propose a very simple geometric criterium to distinguish coupling from entanglement effects among the two set of degrees of freedom associated to each of the disconnected parts of the boundary.

20 pages, Added reference

References in corpus (8)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Static wormhole solution for higher-dimensional gravity in vacuum
• Euclidean Wormholes in String Theory
• Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns
• Holographic real-time non-relativistic correlators at zero and finite temperature
• Strings on AdS Wormholes