A differential equation for a four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
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_{-\frac{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.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- July 2009
- DOI:
- 10.1088/1751-8113/42/30/304011
- arXiv:
- arXiv:0902.1331
- Bibcode:
- 2009JPhA...42D4011F
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- J.Phys.A42:304011,2009