Werner Ruehl,  Technische Universitat Kaiserslautern
AdS/CFT correspondence: Applications and puzzles
Though AdS/CFT correspondence can be considered to be proved in general, some puzzles remain that have to be understood. In conformal harmonic analysis of CFT representations always appear in dual pairs. In AdS-QFT this has been shown to occur in the same way only in some special examples.  It is known that in a perturbative approach to any CFT the critical objects, such as field dimensions in particular their anomalous parts, can be extracted from a system of conformal bootstrap equations (Parisi-Symanzik equations). In the corresponding AdS-QFTs such bootstrap equations must also exist that determine the masses of the fields in terms of power series of the coupling constants. There cannot be a freedom of mass renormalization (to experimental values) as in QED. We propose some applications hitherto not investigated.