A differential equation for a four-point correlation function in Liouville field theory and elliptic four-point conformal blocks

作者：Fateev Vladimir A^*; Litvinov Alexey V; Neveu Andre; Onofri Enrico

来源：Journal of Physics A-Mathematical and Theoretical, 2009, 42(30): 304011.

DOI：10.1088/1751-8113/42/30/304011

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field V(-mb/2). We also introduce and study a class of four-point conformal blocks which can be calculated exactly and represented by finite-dimensional integrals of elliptic theta-functions for an arbitrary intermediate dimension. We also study the bootstrap equations for these conformal blocks and derive integral representations for corresponding four-point correlation functions. A relation between the one-point correlation function of a primary field on a torus and a special four-point correlation function on a sphere is proposed.

• 出版日期2009-7-31