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Exact WKB analysis of ℂℙ1 holomorphic blocks

A preprint version of the article is available at arXiv.

Abstract

We study holomorphic blocks in the three dimensional \( \mathcal{N} \) = 2 gauge theory that describes the ℂℙ1 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 1𝜙1q-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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Correspondence to Sujay K. Ashok.

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ArXiv ePrint: 1907.05031

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Ashok, S.K., Subramanian, P.N.B., Bawane, A. et al. Exact WKB analysis of ℂℙ1 holomorphic blocks. J. High Energ. Phys. 2019, 75 (2019). https://doi.org/10.1007/JHEP10(2019)075

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Keywords

  • Supersymmetric Gauge Theory
  • Chern-Simons Theories
  • Duality in Gauge Field Theories
  • Nonperturbative Effects