• 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}
}
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… 
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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.
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