AdS Dynamics for Massive Scalar Field: exact solutions vs. bulk-boundary propagator

TL;DR

This paper investigates AdS dynamics for massive scalar fields by deriving exact solutions and constructing bulk-boundary propagators, revealing a correspondence between these approaches and analyzing the metric and singularities.

Contribution

It provides a detailed comparison between exact solutions and bulk-boundary propagator methods for massive scalar fields in AdS, introducing a Robertson-Walker-like metric with a horizon.

Findings

Exact solutions correspond one-to-one with bulk-boundary propagator fields

A Robertson-Walker-like metric with a horizon is derived

Singularities at the boundary are explicitly demonstrated

Abstract

AdS dynamics for massive scalar field is studied both by solving exactly the equation of motion and by constructing bulk-boundary propagator. A Robertson-Walker-like metric is deduced from the familiar SO(2,n) invariant metric. The metric allows us to present a time-like Killing vector, which is not only invariant under space-like transformations but also invariant under the isometric transformations of SO(2,n) in certain sense. A horizon appears in this coordinate system. Singularities of field variables at boundary are demonstrated explicitly. It is shown that there is a one-to-one correspondence among the exact solutions and the bulk fields obtained by using the bulk-boundary propagator.