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Exact WKB Analysis of $\mathbb{CP}^1$ Holomorphic Blocks

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arxiv 1907.05031 v3 pith:HGBKOH55 submitted 2019-07-11 hep-th

Sujay K. Ashok , P. N. Bala Subramanian , Aditya Bawane , Dharmesh Jain , Dileep P. Jatkar , Arkajyoti Manna This is my paper · ORCID
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keywords blocksholomorphicmethodsexactmathbbanalysisanalyticanalyze
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abstract

We study holomorphic blocks in the three dimensional ${\mathcal N}=2$ gauge theory that describes the $\mathbb{CP}^1$ model. We apply exact WKB methods to analyze the line operator identities associated to the holomorphic blocks and derive the analytic continuation formulae of the blocks as the twisted mass and FI parameter are varied. The main technical result we utilize is the connection formula for the ${}_1\phi_1$ $q$-hypergeometric function. We show in detail how the $q$-Borel resummation methods reproduce the results obtained previously by using block-integral methods.

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  1. Exact WKB in all sectors II: Potentials with non-degenerate saddles

    hep-th 2025-11 conditional novelty 7.0 of 10

    For generic one-dimensional potentials, the exact spectrum decomposes into as many trans-series sectors as there are distinct local-minimum energy levels, with continuous transitions across barrier tops and discontinu...

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