NDLI: $${SL(2, \mathbb{C})}$$ Chern–Simons Theory and the Asymptotic Behavior of the Colored Jones Polynomial

Content Provider	Springer Nature Link
Author	Gukov, Sergei Murakami, Hitoshi
Copyright Year	2008
Abstract	It has been proposed that the asymptotic behavior of the colored Jones polynomial is equal to the perturbative expansion of the Chern–Simons gauge theory with complex gauge group $${SL(2, \mathbb{C})}$$ on the hyperbolic knot complement. In this note we make the first step toward verifying this relation beyond the semi-classical approximation. This requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern–Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.
Ending Page	98
Page Count	20
Starting Page	79
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	2-3
Volume Number	86
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-11-26
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometric structures on low-dimensional manifolds Eta-invariants, Chern-Simons invariants Mathematical and Computational Physics Determinants and determinant bundles, analytic torsion Knots and links in $S^3$ Geometry A-polynomial Chern–Simons theory colored Jones polynomial Invariants of knots and 3-manifolds Group Theory and Generalizations volume conjecture Statistical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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