Introduction to the Gopakumar-Vafa Large N Duality
Abstract
Gopakumar-Vafa large N duality is a correspondence between Chern-Simons invariants of a link in a 3-manifold and relative Gromov-Witten invariants of a 6-dimensional symplectic manifold relative to a Lagrangian submanifold. We address the correspondence between the Chern-Simons free energy of S^3 with no link and the Gromov-Witten invariant of the resolved conifold in great detail. This case avoids mathematical difficulties in formulating a definition of relative Gromov-Witten invariants, but includes all of the important ideas. There is a vast amount of background material related to this duality. We make a point of collecting all of the background material required to check this duality in the case of the 3-sphere, and we have tried to present the material in a way complementary to the existing literature. This paper contains a large section on Gromov-Witten theory and a large section on quantum invariants of 3-manifolds. It also includes some physical motivation, but for the most part it avoids physical terminology.
Cite
@article{arxiv.math/0701568,
title = {Introduction to the Gopakumar-Vafa Large N Duality},
author = {Dave Auckly and Sergiy Koshkin},
journal= {arXiv preprint arXiv:math/0701568},
year = {2009}
}
Comments
This is the version published by Geometry & Topology Monographs on 21 September 2007