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On modular transformations of non-degenerate toric conformal blocks
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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 B. Ponsot and J. Teschner. We also interpret obtained series representation as a non-perturbative expansion and note that this raises further questions.
Forward citations
Cited by 2 Pith papers
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On the Virasoro Crossing Kernels at Rational Central Charge
At rational central charge, the Virasoro crossing kernels decompose into two admissible square-root-branched kernels; the physical c≤1 kernels are derived for the first time.
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Modular transformations of tau functions and conformal blocks on the torus
The paper derives the modular connection constant for tau functions on the one-punctured torus and obtains an exact closed formula for the c=1 Virasoro modular kernel.
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