Causality and the conformal boundary of AdS in real-time holography

TL;DR

This paper derives explicit formulas relating boundary and bulk fields in Lorentzian AdS space using causality, providing a clear causal picture of the holographic correspondence in real-time holography.

Contribution

It introduces a causality-based derivation of the holographic prescription in Lorentzian AdS, differing from previous Euclidean approaches.

Findings

Unique causal propagator identified

Explicit boundary-bulk field relationship derived

Provides a causal interpretation of the conformal boundary

Abstract

We consider the holographic prescription problem in a (Lorentzian) AdS background, deriving from first principles the explicit formulas that relate the field at infinity with the field in the bulk. In contrast with the previous studies of the "real-time" holography problem, our derivation uses purely classical arguments that involve causality, as in the usual treatment of the holographic prescription problem in Wick-rotated spaces of Euclidean signature. We show that there is a unique propagator that preserves causality and see that this provides a simple picture of the relationship between the bulk manifold and its conformal boundary.