Lorentzian AdS, Wormholes and Holography

TL;DR

This paper explores the structure of two-point functions in the dual QFT of an asymptotically Lorentzian AdS-wormhole, proposing a new way to interpret boundary conditions and distinguish between entanglement and coupling effects.

Contribution

It introduces a novel approach to compute two-point functions in Lorentzian AdS-wormholes, emphasizing boundary value interpretation and a geometric criterion to differentiate entanglement from coupling.

Findings

Boundary values as sources for dual operators are identified.

A simple geometric criterion distinguishes coupling from entanglement.

Normalizable mode ambiguity relates to initial and final states.

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.