Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909318917390336 |
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| author | Desiraju, Harini Ghosal, Promit Prokhorov, Andrei |
| author_facet | Desiraju, Harini Ghosal, Promit Prokhorov, Andrei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_05839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus Desiraju, Harini Ghosal, Promit Prokhorov, Andrei Mathematical Physics Classical Analysis and ODEs Probability 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. |
| title | Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus |
| topic | Mathematical Physics Classical Analysis and ODEs Probability |
| url | https://arxiv.org/abs/2407.05839 |