A note on conformally compactified connection dynamics tailored for anti-de Sitter space

TL;DR

This paper develops a conformal compactification framework within loop quantum gravity to describe asymptotically anti-de Sitter spacetimes using spin networks, facilitating the study of their quantum structure.

Contribution

It introduces a conformal compactification method tailored for AdS spaces in loop quantum gravity, enabling finite-volume descriptions via spin networks.

Findings

Finite-volume conformal compactification of AdS space

Spin network states effectively describe the compactified geometry

Applicable to asymptotically AdS black hole solutions

Abstract

A framework conceptually based on the conformal techniques employed to study the structure of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions.