Exact WKB, Nonabelianization and Conformal Blocks

par Qianyu Hao (Université de Genève)

lundi 26 févr. 2024, 14:30 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seminar on  Quantum and Modularity Resurgence

In this talk, I will review the exact WKB approach used in the QFT/ODE correspondence related to the NS phase of the Ω-background. By AGT correspondence, those QFT’s are related to c = ∞ CFTs. In particular, I will focus on the Stokes graph, also known as the spectral network in physics. The spectral network plays an essential role in the exact WKB and the nonabelianization of SL(N,C) flat connections. We find that the very same structure also exists at the self dual phase of the Ω-background, which is the c = 1 Liouville CFT by AGT correspondence. I will introduce our work on nonabilianization of the Virasoro conformal blocks using Heisenberg conformal blocks with the key ingredient of spectral networks. This is analogous to the nonabelianization of SL(2, C) flat connections by the GL(1, C) connections. This is a joint work in progress with Andrew Neitzke.

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