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SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial

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arxiv math/0608324 v2 pith:M5GF7EJL submitted 2006-08-14 math.GT hep-thmath.QA

Sergei Gukov , Hitoshi Murakami This is my paper · ORCID
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keywords coloredjonespolynomialasymptoticbehaviorchern-simonstheorygauge
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We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison 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.

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    A new arcade-based planarization technique plus the Kuperberg bracket yields a closed system of classical relations toward su3 A-polynomials, demonstrated on the trefoil.

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