Tenfold Way for Holography : AdS/CFT and Beyond

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 $\mathcal{G}$. 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.

24 pages, 5 tables, Latex2e; v2,3: corrected typos, v4 revised as accepted in IJMPA

References in corpus (10)

• Towards a derivation of holographic entanglement entropy
• Holography from Conformal Field Theory
• Holographic c-theorems in arbitrary dimensions
• Writing CFT correlation functions as AdS scattering amplitudes
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Galilean Conformal Algebras and AdS/CFT
• Symmetries of Holographic Minimal Models
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Tenfold Way for Quadratic Lindbladians
• The all loop AdS4/CFT3 Bethe ansatz