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Exact WKB analysis of ℂℙ1 holomorphic blocks

Journal of High Energy Physics volume 2019, Article number: 75 (2019) Cite this article

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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Authors and Affiliations

  1. Institute of Mathematical Sciences, Homi Bhabha National Institute (HBNI), IV Cross Road, C. I. T. Campus, Taramani, Chennai, 600113, India

    Sujay K. Ashok, P. N. Bala Subramanian & Arkajyoti Manna

  2. Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India

    Aditya Bawane

  3. Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata, 700064, India

    Dharmesh Jain

  4. Harish-Chandra Research Institute, Homi Bhabha National Institute (HBNI), Chhatnag Road, Jhusi, Allahabad, 211019, India

    Dileep P. Jatkar

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  1. Sujay K. Ashok
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  2. P. N. Bala Subramanian
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  3. Aditya Bawane
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  4. Dharmesh Jain
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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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  • DOI: https://doi.org/10.1007/JHEP10(2019)075

Keywords

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