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

1999/02/28 by Arkady L. Kholodenko · 1 citation
Mathematics · Physics and Astronomy · #Analytic and geometric function theory #Boundary (topology) #Conformal map #Differential geometry #Extension (predicate logic) #Field (mathematics) #Geometric and Algebraic Topology #Holography #Limit (mathematics) #Mathematical Dynamics and Fractals #Work (physics) #hep-th

paper · pdf · doi:10.1016/s0393-0440(00)00010-3

published as J.Geom.Phys.35:193-238,2000 · 62 pages, 5 figures

arxiv created 1999/06/24 · openalex publication_date 2000/09/01 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) 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. Known in physical literature objections against such extension are removed and the possibility of an extension is convincingly demonstrated.

Citations

• Quasiconformal 4-manifolds
• Finite dimensional Teichmüller spaces and generalizations
• Quantum field theory and the Jones polynomial
• Infinite conformal symmetry in two-dimensional quantum field theory
• The boundary correspondence under quasiconformal mappings
• The Large Scale Structure of Space-Time
• The density at infinity of a discrete group of hyperbolic motions
• Einstein metrics with prescribed conformal infinity on the ball
• Uniformization, Moduli, and Kleinian Groups†
• The world as a hologram
• Classical and quantum conformal field theory
• Breaking of conformal symmetry in the AdS/CFT correspondence
• On Unitary Representations of the Group of De Sitter Space
• Conformal Field Theory
• The large N limit of superconformal field theories and supergravity

Cited by

• New strings for old Veneziano amplitudes