The Hadamard Function and the Feynman Propagator in the AdS/CFT Correspondence

TL;DR

This paper constructs and analyzes the retarded Green and Hadamard functions in Lorentzian AdS spacetime, examining their singularity structures and boundary limits to enhance understanding of the AdS/CFT correspondence.

Contribution

It provides explicit mode-integrated constructions of Green functions in Lorentzian AdS and explores their singularity structures and boundary behavior, advancing the theoretical framework of AdS/CFT.

Findings

Explicit retarded Green and Hadamard functions in Lorentzian AdS

Analysis of singularity structures of the Feynman propagator

Boundary limits recover bulk-boundary and boundary correlators

Abstract

We construct the retarded Green function and the Hadamard function in the Lorentzian (d+1)-dimensional anti-de Sitter spacetime for the Poincar\'e coordinate by performing the mode integration directly. We explore the structure of singularities for the position-space Feynman propagator derived from them. The boundary scaling limits of the bulk Feynman propagator yield the bulk-boundary propagator and the boundary conformal correlation function with an extra factor.