Lorentzian AdS geometries, wormholes, and holography

We investigate the structure of two-point functions for the quantum field theory dual to an asymptotically Lorentzian Anti de Sitter (AdS) wormhole. The bulk geometry is a solution of five-dimensional second-order Einstein-Gauss-Bonnet gravity and causally connects two asymptotically AdS spacetimes. We revisit the Gubser-Klebanov-Polyakov-Witten prescription for computing two-point correlation functions for dual quantum field theories operators O in Lorentzian signature and we propose to express the bulk fields in terms of the independent boundary values phi(+/-)(0) 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-+/- and we argue that, apart from the possibility of entanglement, there exists a coupling between the degrees of freedom living 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 criterion to distinguish coupling from entanglement effects among two sets of degrees of freedom associated with each of the disconnected parts of the boundary.