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

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

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...

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Veröffentlicht in:arXiv.org 2024-09
Hauptverfasser: Desiraju, Harini, Ghosal, Promit, Prokhorov, Andrei
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Lame functions
Toruses
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description 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 Lamé 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.
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Toruses
title Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus
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