Easy Holography

TL;DR

This paper explores how infinite-dimensional asymptotic symmetry groups in gravity theories are crucial for holographic descriptions and black hole entropy, using simple models in AdS spaces to illustrate these ideas.

Contribution

It introduces a toy model demonstrating the role of asymptotic symmetry groups in holography and black hole entropy, extending insights to various AdS spaces.

Findings

Asymptotic symmetry groups explain the entropy area law in 2D AdS.

Similar symmetry considerations apply in 3D AdS space.

The approach's limitations in higher dimensions are addressed by alternative spaces.

Abstract

It is argued that the role of infinite dimensional asymptotic symmetry groups in gravity theories are essential for a holographic description of gravity and possibly to a resolution of the black hole information paradox. I present a simple toy model in two dimensional hyperbolic/ anti-de Sitter (AdS) space and describe, by very elementary considerations, how the asymptotic symmetry group is responsible for the entropy area law. Similar results apply also in three dimensional AdS space. The failure of the approach in higher dimensional AdS spaces is explained and resolved by considering other asymptotically noncompact homogeneous spaces.