A differential equation for a fourpoint correlation function in Liouville field theory and elliptic fourpoint conformal blocks
Abstract
Liouville field theory on a sphere is considered. We explicitly derive a differential equation for fourpoint correlation functions with one degenerate field V_{\frac{mb}{2}} . We also introduce and study a class of fourpoint conformal blocks which can be calculated exactly and represented by finitedimensional integrals of elliptic thetafunctions for an arbitrary intermediate dimension. We also study the bootstrap equations for these conformal blocks and derive integral representations for corresponding fourpoint correlation functions. A relation between the onepoint correlation function of a primary field on a torus and a special fourpoint correlation function on a sphere is proposed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 July 2009
 DOI:
 10.1088/17518113/42/30/304011
 arXiv:
 arXiv:0902.1331
 Bibcode:
 2009JPhA...42D4011F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 J.Phys.A42:304011,2009