Letters in Mathematical Physics

, Volume 86, Issue 2–3, pp 79–98 | Cite as

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

  • Sergei GukovEmail author
  • Hitoshi Murakami


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.

Mathematics Subject Classification (2000)

Primary 57M27 57M25 57M50 58J28 58J52 


colored Jones polynomial volume conjecture A-polynomial Chern–Simons theory 


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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Department of Physics and MathematicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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