Anti de Sitter Holography via Sekiguchi Decomposition

TL;DR

This paper explores anti de Sitter holography in higher dimensions using Sekiguchi decomposition, providing a group-theoretic framework for bulk-boundary correspondence in a generalized setting.

Contribution

It introduces a novel group-theoretic approach to anti de Sitter holography by representing the bulk space as a homogeneous space via Sekiguchi decomposition.

Findings

Established the homogeneous space G/H = SO(q,2)/SO(q,1) for the bulk

Extended holography framework to general (q+1)-dimensional anti de Sitter spaces

Provided foundational group-theoretic tools for future holography research

Abstract

In the present paper we start consideration of anti de Sitter holography in the general case of the (q+1)-dimensional anti de Sitter bulk with boundary q-dimensional Minkowski space-time. We present the group-theoretic foundations that are necessary in our approach. Comparing what is done for q=3 the new element in the present paper is the presentation of the bulk space as the homogeneous space G/H = SO(q,2)/SO(q,1), which homogeneous space was studied by Sekiguchi.