WKB-asymptotics for multipoint Virasoro conformal blocks and applications

TL;DR

This paper derives WKB asymptotics for multipoint Virasoro conformal blocks on the sphere, enabling new analytical and numerical approaches in conformal field theory and string theory applications.

Contribution

It introduces a novel WKB-based asymptotic method for multipoint Virasoro blocks, extending classical techniques to complex conformal configurations.

Findings

Asymptotic expressions match known 5-point block results

Enables generalization of Zamolodchikov's elliptic recursion

Facilitates numerical evaluation in minimal string theory

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 WKB method for "classical BPZ equation", which is used to study (classical) Virasoro blocks via 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 5-point blocks in special cases and the usual series expansion of Virasoro blocks computed using AGT correspondence.