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

Sergei Gukov, Hitoshi Murakami

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

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) 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.

Original languageEnglish
Pages (from-to)79-98
Number of pages20
JournalLetters in Mathematical Physics
Volume86
Issue number2-3
DOIs
Publication statusPublished - 2008 Dec
Externally publishedYes

Keywords

  • A-polynomial
  • Chern-Simons theory
  • Colored Jones polynomial
  • Volume conjecture

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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