On modular transformations of toric conformal blocks
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- Nemkov, N. J. High Energ. Phys. (2015) 2015: 39. doi:10.1007/JHEP10(2015)039
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We derive and solve the difference equations on the toric modular kernel following from the consistency relations in the fusion algebra. The result is explicit and simple series expansion for the toric modular kernel of non-degenerate Virasoro conformal blocks. We show that this expansion is equivalent to the celebrated integral representation due to J. Teschner.