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WKB asymptotics for multipoint Virasoro conformal blocks and applications

Aleksandr Artemev1,2,* and Dmitry Khromov1,2,3

  • *Contact author: artemev.aa@phystech.edu
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Phys. Rev. D 114, 045002 – Published 4 August, 2026

DOI: https://doi.org/10.1103/9y4x-9b4p

Abstract

We study multipoint Virasoro conformal blocks on the sphere in the comb channel. We arrive at the asymptotic expression for these blocks at large intermediate dimensions, applying the WKB method for the “classical Belavin-Polyakov-Zamolodchikov equation,” which is used to study (classical) Virasoro blocks via the monodromy method. Several applications of this asymptotic are discussed, such as the possibility to generalize Zamolodchikov’s elliptic recursion and numerical evaluation of amplitudes in minimal string theory. Our expressions pass nontrivial checks, such as agreement with known exact expressions for five-point blocks in special cases and the usual series expansion of Virasoro blocks computed using Alday-Gaiotto-Tachikawa correspondence.

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Phys. Rev. D 114, 045002– Published 4 August, 2026
  • Received 2 April 2026
  • Accepted 14 July 2026
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