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

Abstract

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.

15 pages, 7 figures

References in corpus (1)

• An analytic version of the Melvin-Morton-Rozansky Conjecture

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• The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory