Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
High Energy Physics - Theory
2009-07-17 v3
Abstract
Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field . We introduce and study also a class of four-point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta-functions for arbitrary intermediate dimension. We study also 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.
Cite
@article{arxiv.0902.1331,
title = {Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks},
author = {V. A. Fateev and A. V. Litvinov and A. Neveu and E. Onofri},
journal= {arXiv preprint arXiv:0902.1331},
year = {2009}
}