Tenfold Way for Holography : AdS/CFT and Beyond

TL;DR

This paper develops a mathematical framework for extending holography beyond conformal theories using group theory and Lie algebra decompositions, broadening the scope of AdS/CFT correspondence.

Contribution

It introduces a systematic approach employing all ten families of classical real semisimple Lie groups and algebras to generalize holography beyond conformal settings.

Findings

Utilizes Iwasawa, Bruhat, and Sekiguchi decompositions for group analysis.

Applies methods to exceptional real semisimple Lie algebras.

Establishes foundational structures for generalized holography.

Abstract

The main purpose of the present paper is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten families of classical real semisimple Lie groups $G$ and Lie algebras $\cal G$. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi-like decomposititions. The same analysis is applied to the exceptional real semisimple Lie algebras.