Proof of Zamolodchikov conjecture for semi-classical conformal blocks on torus

Autor:	Desiraju, Harini, Ghosal, Promit, Prokhorov, Andrei
Rok vydání:	2024
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	In 1986, Zamolodchikov conjectured an exponential structure for the semi-classical limit of conformal blocks on a sphere. This paper provides a rigorous proof of the analog of Zamolodchikov conjecture for Liouville conformal blocks on a one-punctured torus, using their probabilistic construction and show the existence of a positive radius of convergence of the semi-classical limit. As a consequence, we obtain a closed form expression for the solution of the Lam\'e equation, and show a relation between its accessory parameter and the classical action of the non-autonomous elliptic Calogero-Moser model evaluated at specific values of the solution. Comment: 51 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.05839 Zobrazit plný text záznamu View this record from Arxiv