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arXiv · 2407.05839

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

Harini Desiraju·Promit Ghosal·Andrei Prokhorov
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Abstract

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.

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Harini Desiraju, Promit Ghosal, Andrei Prokhorov. 2024-07-08. Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus. https://arxiv.org/abs/2407.05839

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