Boundary conformal field theories, limit sets of Kleinian groups and holography

In this paper, based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Friedman et al. (Nuclear Phys. B 456 (1999) 96-118) are reproduced and broadly generalized. Among many new results, the possibility of extension of work of Belavin, Polyakov and Zamolodchikov to higher dimensions is investigated. Objections known in the physical literature against such an extension are removed and the possibility of an extension is convincingly demonstrated. (C) 2000 Elsevier Science B.V. All rights reserved.