Asymptotically anti-de Sitter space-times: symmetries and conservation laws revisited

TL;DR

This paper revisits the symmetries and conservation laws in asymptotically anti-de Sitter space-times, explicitly connecting boundary conformal symmetries with bulk Killing vectors and deriving conditions for finite conserved charges.

Contribution

It explicitly verifies the correspondence between asymptotic Killing vectors and boundary conformal Killing vectors in static coordinates for AdS space-times and derives fall-off conditions for metric perturbations.

Findings

Confirmed the one-to-one correspondence between asymptotic Killing vectors and boundary conformal Killing vectors.

Derived fall-off conditions ensuring finite conserved charges.

Clarified the symmetry structure of asymptotically AdS space-times.

Abstract

In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat metric induced on the boundary. The fall-off conditions for the metric perturbations that guarantee finiteness of the associated conserved charges are derived.