Asymptotic Form of Gopakumar-Vafa Invariants from Instanton Counting
arXiv:hep-th/0311220 · doi:10.1016/j.nuclphysb.2004.01.021
Abstract
We study the asymptotic form of the Gopakumar-Vafa invariants at all genera for Calabi-Yau toric threefolds which have the structure of fibration of the A_n singularity over P^1. We claim that the asymptotic form is the inverse Laplace transform of the corresponding instanton amplitude in the prepotential of N=2 SU(n+1) gauge theory coupled to external graviphoton fields, which is given by the logarithm of the Nekrasov's partition function.
22 pages, 2 figures; (v2) typos corrected