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

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arxiv 2407.05839 v3 pith:UK63AH4O submitted 2024-07-08 math-ph math.CAmath.MPmath.PR

Harini Desiraju , Promit Ghosal , Andrei Prokhorov This is my paper
classification math-phmath.CAmath.MPmath.PR
keywords blocksconformalsemi-classicalzamolodchikovconjecturelimitproofsolution
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modular transformations of tau functions and conformal blocks on the torus

    math-ph 2025-08 conditional novelty 8.0 of 10

    The paper derives the modular connection constant for tau functions on the one-punctured torus and obtains an exact closed formula for the c=1 Virasoro modular kernel.

  2. Eigenfunctions of deformed Schr\"odinger equations

    hep-th 2025-11 conditional novelty 7.0 of 10

    Explicit entire eigenfunctions are constructed for the difference operators 2Λ^N cosh(p)+V_N(x) with arbitrary polynomial potential; they become square-integrable only at a discrete set of energies.

  3. Blowing-up the edge: connection formulae and stability chart of the Lam\'e equation

    hep-th 2025-07 conditional novelty 7.0 of 10

    The paper derives the resummed Nekrasov-Shatashvili free energy from blow-up equations and uses it to compute the band-gap structure, connection formulas, and stability chart of the Lamé equation.

  4. 2D CFT and efficient Bethe ansatz for exactly solvable Richardson-Gaudin models

    hep-th 2025-07 conditional novelty 3.0 of 10

    The paper identifies the Richardson Yang-Yang function with a Gaiotto-Witten irregular Virasoro block and provides a numerical solver for the Bethe equations of Richardson-Gaudin models.

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