Introduction to the Gopakumar-Vafa Large N Duality

Dave Auckly; Sergiy Koshkin

doi:10.2140/gtm.2006.8.195

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Introduction to the Gopakumar-Vafa Large N Duality

Dave Auckly·Sergiy Koshkin

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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.

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BibTeX RIS

Dave Auckly, Sergiy Koshkin. 2009-03-13. Introduction to the Gopakumar-Vafa Large N Duality. https://doi.org/10.2140/gtm.2006.8.195

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