• Corpus ID: 227239277

# Peacock patterns and resurgence in complex Chern-Simons theory

@article{Garoufalidis2020PeacockPA,
title={Peacock patterns and resurgence in complex Chern-Simons theory},
author={Stavros Garoufalidis and Jie Gu and Marcos Mari{\~n}o},
journal={arXiv: Geometric Topology},
year={2020}
}
• Published 30 November 2020
• Mathematics, Physics
• arXiv: Geometric Topology
The partition function of complex Chern-Simons theory on a 3-manifold with torus boundary reduces to a finite dimensional state-integral which is a holomorphic function of a complexified Planck's constant $\tau$ in the complex cut plane and an entire function of a complex parameter $u$. This gives rise to a vector of factorially divergent perturbative formal power series whose Stokes rays form a peacock-like pattern in the complex plane. We conjecture that these perturbative series are…
6 Citations

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## References

SHOWING 1-10 OF 80 REFERENCES
The Resurgent Structure of Quantum Knot Invariants
• Medicine, Physics
Communications in mathematical physics
• 2021
It is conjectured that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte–Gaiotto–Gukov 3D-index, and thus is given by a counting of BPS states.
Holomorphic blocks in three dimensions
• Physics
• 2012
A bstractWe decompose sphere partition functions and indices of three-dimensional N$$\mathcal{N}$$ = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The
The quantum content of the gluing equations
• Mathematics, Physics
• 2012
The gluing equations of a cusped hyperbolic 3-manifold $M$ are a system of polynomial equations in the shapes of an ideal triangulation $\calT$ of $M$ that describe the complete hyperbolic structure
Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,ℂ), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds.
Chern-Simons theory, analytic continuation and arithmetic
The purpose of the paper is to introduce some conjectures re- garding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the
Divergent Series, Summability and Resurgence I: Monodromy and Resurgence
• Mathematics
• 2016
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential
Analytic Continuation Of Chern-Simons Theory
The title of this article refers to analytic continuation of three-dimensional ChernSimons gauge theory away from integer values of the usual coupling parameter k, to explore questions such as the
Exact eigenfunctions and the open topological string
• Physics, Mathematics
• 2016
Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the
Resurgence in complex Chern-Simons theory
• Physics, Mathematics
• 2016
We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of