2003/09/30 by F. A. Dolan, F.A. Dolan, H. Osborn · 17 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conformal symmetry #Differential equation #Differential operator #Dimension (graph theory) #Hypergeometric function #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Operator product expansion #Ordinary differential equation #Partial differential equation #Primary field #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Symbol of a differential operator #Weyl transformation #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2003.11.016
published as Nucl.Phys. B678 (2004) 491-507 · 17 pages, uses harvmac, v2 correction to eq. 2.20
openalex publication_date 2003/12/02 · arxiv created 2016/03/09 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for O(d,2) succinct expressions are found for the functions, conformal partial waves, representing the contribution of an operator of arbitrary scale dimension Δ and spin ℓ together with its descendants to conformal four point functions for d=4, recovering old results, and also for d=6. The results are expressed in terms of ordinary hypergeometric functions of variables x,z which are simply related to the usual conformal invariants. An expression for the conformal partial wave amplitude valid for any dimension is also found in terms of a sum over two variable symmetric Jack polynomials which is used to derive relations for the conformal partial waves.