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

Gukov, Sergei and Murakami, Hitoshi (2008) SL(2,C) Chern–Simons Theory and the Asymptotic Behavior of the Colored Jones Polynomial. Letters in Mathematical Physics, 86 (2-3). pp. 79-98. ISSN 0377-9017. https://resolver.caltech.edu/CaltechAUTHORS:20160511-094807499

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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,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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11005-008-0282-3DOIArticle
http://link.springer.com/article/10.1007%2Fs11005-008-0282-3PublisherArticle
http://arxiv.org/abs/math/0608324arXivDiscussion Paper
ORCID:
AuthorORCID
Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2008 Springer. Received: 7 July 2007; Revised: 18 August 2008; Accepted: 6 November 2008. The authors would like to thank Jérôme Dubois, Stavros Garoufalidis, and Toshiaki Hattori for helpful conversations. It is also a pleasure to thank the organizers of the conference “Around the Volume Conjecture” at Columbia University in March 2006 and the conference “Modular Forms and String Duality” at Banff in June 2006, which stimulated much of this work. This work was supported in part by the DOE under grant number DE-FG03-92-ER40701, in part by RFBR grant 04-02-16880, and in part by the grant for support of scientific schools NSh-8004.2006.2 (S.G.), and in part by Grant-in-Aid for Scientific Research (B) (15340019) (H.M.).
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Russian Foundation for Basic Research04-02-16880
UNSPECIFIEDNSh-8004.2006.2
Japan Society for the Promotion of Science (JSPS)15340019
Subject Keywords:colored Jones polynomial, volume conjecture, A-polynomial, Chern–Simons theory
Issue or Number:2-3
Classification Code:Mathematics Subject Classification (2000): Primary 57M27, 57M25, 57M50, 58J28, 58J52
Record Number:CaltechAUTHORS:20160511-094807499
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160511-094807499
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66981
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 May 2016 16:57
Last Modified:09 Mar 2020 13:18

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