We derive and solve the difference equations on the toric modular kernelfollowing from the consistency relations in the fusion algebra. The result isexplicit and simple series expansion for the toric modular kernel ofnon-degenerate Virasoro conformal blocks. We show that this expansion isequivalent to the celebrated integral representation due to B. Ponsot and J.Teschner. We also interpret obtained series representation as anon-perturbative expansion and note that this raises further questions.
展开▼
