On "Dotsenko-Fateev" representation of the toric conformal blocks

Details On "Dotsenko-Fateev" representation of the toric conformal blocks On "Dotsenko-Fateev" representation of the toric conformal blocks

2010-10-08

arxiv.org/abs/1010.1734v1

J.Phys.A44:085401,2011

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/1751-8113/44/8/085401

We demonstrate that the recent ansatz of arXiv:1009.5553, inspired by the original remark due to R.Dijkgraaf and C.Vafa, reproduces the toric conformal blocks in the same sense that the spherical blocks are given by the integral representation of arXiv:1001.0563 with a peculiar choice of open integration contours for screening insertions. In other words, we provide some evidence that the toric conformal blocks are reproduced by appropriate beta-ensembles not only in the large-N limit, but also at finite N. The check is explicitly performed at the first two levels for the 1-point toric functions. Generalizations to higher genera are briefly discussed.

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