|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Peacock patterns and resurgence in complex Chern-Simons theory | | Stavros Garoufalidis
; Jie Gu
; Marcos Marino
; | | Date: |
30 Nov 2020 | | Abstract: | 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 $ au$ 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 resurgent, their
trans-series involve two non-perturbative variables, their Stokes automorphism
satisfies a unique factorization property and that it is given explicitly in
terms of a fundamental matrix solution to a (dual) linear $q$-difference
equation. We further conjecture that a distinguished entry of the Stokes
automorphism matrix is the 3D-index of Dimofte-Gaiotto-Gukov. We provide proofs
of our statements regarding the $q$-difference equations and their properties
of their fundamental solutions and illustrate our conjectures regarding the
Stokes matrices with numerical calculations for the two simplest hyperbolic
$4_1$ and $5_2$ knots. | | Source: | arXiv, 2012.00062 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER