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.

A differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks / VLADIMIR A., Fateev; ALEXEY V., Litvinov; Andre, Neveu; Onofri, Enrico. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 42:(2009), pp. 1-29. [10.1088/1751-8113/42/30/304011]

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

ONOFRI, Enrico
2009

Abstract

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.
A differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks / VLADIMIR A., Fateev; ALEXEY V., Litvinov; Andre, Neveu; Onofri, Enrico. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 42:(2009), pp. 1-29. [10.1088/1751-8113/42/30/304011]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2279379
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