Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks Auteur(s): Fateev V., Litvinov A. V., Neveu A., Onofri Enrico (Article) Publié: Journal Of Physics A: Mathematical And Theoretical, vol. 42 p.304011 (2009) Texte intégral en Openaccess : Ref HAL: hal-00379184_v1 Ref Arxiv: 0902.1331 DOI: 10.1088/1751-8113/42/30/304011 WoS: 000267943000012 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote 41 Citations Résumé: Liouville field theory on a sphere is considered. We explicitly derive adifferential equation for four-point correlation functions with one degeneratefield $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-pointconformal blocks which can be calculated exactly and represented by finitedimensional integrals of elliptic theta-functions for arbitrary intermediatedimension. We study also the bootstrap equations for these conformal blocks andderive integral representations for corresponding four-point correlationfunctions. A relation between the one-point correlation function of a primaryfield on a torus and a special four-point correlation function on a sphere isproposed. Commentaires: 29 pp. |