Tenfold way for holography: AdS/CFT and beyond

Abstract

The main purpose of this 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 [Formula: see text] and Lie algebras [Formula: see text]. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi-like decompositions. The same analysis is applied to the exceptional real semisimple Lie algebras.