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arXiv · 2607.09177

A note on Zamolodchikov's recursion relation for the torus conformal block and its light limit

Armen Poghosyan·Hasmik Poghosyan
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Abstract

In this paper, we review the Zamolodchikov-like recursion relations for torus one-point conformal blocks in both Liouville and $A_2$ Toda theories. Starting from these relations, we derive the corresponding recursion relations in the light asymptotic limit. In Liouville theory, the light-limit recursion reproduces the known expression for the one-point light conformal block in terms of the Gauss hypergeometric function. For $A_2$ Toda theory, our recursion relation provides a new, efficient method for explicit calculations, and we have verified that it is in full agreement with previously known results in the literature.

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Armen Poghosyan, Hasmik Poghosyan. 2026-07-10. A note on Zamolodchikov's recursion relation for the torus conformal block and its light limit. https://arxiv.org/abs/2607.09177

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