Facts and Fictions about Anti deSitter Spacetimes with Local Qantum Matter

Abstract

It is natural to analyse the AdS${}_{d+1}$-CQFT${}_d$ correspondence in the context of the conformal- compactification and covering formalism. In this way one obtains additional inside about Rehren's rigorous algebraic holography in connection with the degree of freedom issue which in turn allows to illustrates the subtle but important differences beween the original string theory-based Maldacena conjecture and Rehren's theorem in the setting of an intrinsic field-coordinatization-free formulation of algebraic QFT. I also discuss another more generic type of holography related to light fronts which seems to be closer to 't Hooft's original ideas on holography. This in turn is naturally connected with the generic concept of ``Localization Entropy'', a quantum pre-form of Bekenstein's classical black-hole surface entropy.

Comments: this final version is identical to the one which appeared in Commun. Math. Phys. 219, (2001) 57-76, an issue of CMP dedicated to the memory of Harry Lehmannn