Convergence of classical conformal blocks

Pietro Menotti

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arXiv · 2512.18666

Convergence of classical conformal blocks

Pietro Menotti

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Abstract

We give a recursive method to compute the classical conformal blocks in Liouville field theory. The values of the expansion coefficients are given by an algebraic scheme which works to all orders. The algebraic expression of the intervening matrices are explicitly given. With regard to the problem of the convergence of the series we rigorously prove that it has a finite (non zero) convergence radius. We then comment on the relation of the conformal block problem with the Riemann-Hilbert problem.

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Pietro Menotti. 2025-12-21. Convergence of classical conformal blocks. https://arxiv.org/abs/2512.18666

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