Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-08
J.Phys.A42:304011,2009
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
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 $V_{-\frac{mb}{2}}$. 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.
Fateev Vladimir A.
Litvinov A. V.
Neveu A.
Onofri Enrico
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