Zamolodchikov-type copnjecture for irregular Heun equations (Kohei IWAKI, University of Tokyo)

13.05.2026 14:30

The Heun equation is a Fuchsian differential equation on the Riemann sphere with four regular singular points, and it contains an accessory parameter that cannot be determined solely from the local monodromy data. A famous conjecture due to Zamolodchikov states that the large central charge limit of the Virasoro conformal block exists, and that this limit yields the accessory parameter. In this talk, we extend this conjecture to all confluent Heun equations with irregular singularities obtained through confluence procedures, and present supporting computational evidence. More specifically, we investigate the relation between the accessory parameters of irregular Heun equations and the Voros periods arising in exact WKB analysis, and compare them with the conformal blocks (or candidates thereof) derived from bilinear identities by Bonelli—Shchechkin—Tanzini. Our results may be regarded as a generalization of earlier works by Mironov—Morozov, Piatek—Pietrykowski, Lisovyy—Naidiuk and others. This is joint work with Nagoya (Kanazawa University) and Shukuta (The University of Tokyo).

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Conseil Général 7-9, Room 1-15, Séminaire de Physique mathématique

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