发表机构
Yerevan Physics Institute（叶里万物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究刘维尔和\(A_2\)托达理论中环面单点共形块的类扎莫洛德奇科夫递归关系，推导其光渐近极限下的关系，为\(A_2\)托达理论提供新计算方法，结果与文献一致。
AI 中文摘要
本文回顾了刘维尔和\(A_2\)托达理论中环面单点共形块的类扎莫洛德奇科夫递归关系。从这些关系出发，我们推导了光渐近极限下的相应递归关系。在刘维尔理论中，光极限递归重现了用高斯超几何函数表示的单点光共形块的已知表达式。对于\(A_2\)托达理论，我们的递归关系提供了一种新的显式计算有效方法，并验证其与文献中先前已知结果完全一致。
英文摘要
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.
Comments21 pages, major changes
