Summability for State Integrals of hyperbolic knots

Veronica Fantini; Campbell Wheeler

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arXiv · 2410.20973

Summability for State Integrals of hyperbolic knots

Veronica Fantini·Campbell Wheeler

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Abstract

We prove conjectures of Garoufalidis-Gu-Mari\~no that perturbative series associated with the hyperbolic knots $4_1$ and $5_2$ are resurgent and Borel summable. In the process, we give an algorithm that can be used to explicitly compute the Borel-Laplace resummation as a combination of state integrals of Andersen-Kashaev. This gives a complete description of the resurgent structure in these examples and allows for explicit computations of Stokes constants.

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BibTeX RIS

Veronica Fantini, Campbell Wheeler. 2024-10-28. Summability for State Integrals of hyperbolic knots. https://arxiv.org/abs/2410.20973

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