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Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres Σ(2,3,6n+5)

Wu, David H. (2021) Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres Σ(2,3,6n+5). Journal of High Energy Physics, 2021 (2). Art. No. 8. ISSN 1126-6708.

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Ẑ-invariants, which can reconstruct the analytic continuation of the SU(2) Chern-Simons partition functions via Borel resummation, were discovered by GPV and have been conjectured to be a new homological invariant of 3-manifolds which can shed light onto the superconformal and topologically twisted index of 3d N = 2 theories proposed by GPPV. In particular, the resurgent analysis of Ẑ has been fruitful in discovering analytic properties of the WRT invariants. The resurgent analysis of these Ẑ-invariants has been performed for the cases of Σ(2, 3, 5), Σ(2, 3, 7) by GMP, Σ(2, 5, 7) by Chun, and, more recently, some additional Seifert manifolds by Chung and Kucharski, independently. In this paper, we extend and generalize the resurgent analysis of Ẑ on a family of Brieskorn homology spheres Σ(2, 3, 6n + 5) where n ∈ ℤ₊ and 6n + 5 is a prime. By deriving Ẑ for Σ(2, 3, 6n + 5) according to GPPV and Hikami, we provide a formula where one can quickly compute the non-perturbative contributions to the full analytic continuation of SU(2) Chern-Simons partition function.

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Wu, David H.0000-0003-4587-0280
Additional Information:© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: October 27, 2020; Accepted: December 21, 2020; Published: February 1, 2021. The author would like to thank Sergei Gukov for his invaluable comments and discussions during the project.
Funding AgencyGrant Number
Subject Keywords:Chern-Simons Theories, Nonperturbative Effects, Solitons Monopoles and Instantons, Field Theories in Lower Dimensions
Issue or Number:2
Record Number:CaltechAUTHORS:20210120-144315283
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Official Citation:Wu, D.H. Resurgent analysis of SU(2) Chern-Simons partition function on Brieskorn spheres Σ(2, 3, 6n + 5). J. High Energ. Phys. 2021, 8 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107602
Deposited By: Tony Diaz
Deposited On:20 Jan 2021 23:06
Last Modified:02 Feb 2021 18:46

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