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

Creators: Gukov, Sergei; Murakami, Hitoshi

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.

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.).

Attached Files

Published - art_3A10.1007_2Fs11005-008-0282-3.pdf

Submitted - 0608324.pdf

Files

0608324.pdf

Files (735.3 kB)

Name	Size	Download all
0608324.pdf md5:5e905315a8f31e3634685ee33098f5c5	293.0 kB	Preview Download
art_3A10.1007_2Fs11005-008-0282-3.pdf md5:d49c2892cce43922cbfd78b30e75cd6f	442.3 kB	Preview Download

Additional details

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes