Resurgence in complex Chern-Simons theory at generic levels

A bstract In this note we study the resurgent structure of sl (2 , ℂ) Chern-Simons state integral model on knot complements S 3 \ 4 1 , S 3 \ 5 2 with generic discrete level k ≥ 1 and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of...

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Bibliographic Details
Published in:The journal of high energy physics 2023-05, Vol.2023 (5), p.86-46, Article 86
Main Authors: Duan, Zhihao, Gu, Jie
Format: Article
Language:English
Subjects:
Asymptotic series
Chern-Simons Theories
Classical and Quantum Gravitation
Elementary Particles
Field theory (physics)
High energy physics
Knots
Nonperturbative Effects
Physics
Physics and Astronomy
Polynomials
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
Saddle points
String Theory
Thermal expansion
Topological Field Theories
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Summary:A bstract In this note we study the resurgent structure of sl (2 , ℂ) Chern-Simons state integral model on knot complements S 3 \ 4 1 , S 3 \ 5 2 with generic discrete level k ≥ 1 and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of the knot extended by the holonomy parameter. Despite increasing complication of the asymptotic series as the level k increases, the resurgent structure of the asymptotic series is universal: both the distribution of Borel plane singularities and the associated Stokes constants are independent of the level k .
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP05(2023)086