A note on Zamolodchikov's recursion relation for the torus conformal block and its light limit
Year: 2026
Type: preprint
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. Last but not least, we present closed-form expressions for the coefficients of the insertion-point expansion for both the generic and light $A_2$ Toda one-point blocks.
Source: arXiv (Cornell University)
Authors: Poghosyan, Armen, Poghosyan, Hasmik
Institution: A. Alikhanyan National Laboratory
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168179870