Topological Strings, Instantons and Asymptotic Forms of Gopakumar-Vafa Invariants
arXiv:hep-th/0312090
Abstract
We calculate the topological string amplitudes of Calabi-Yau toric threefolds corresponding to 4D, N=2, SU(2) gauge theory with N_f=0,1,2,3,4 fundamental hypermultiplets by using the method of the geometric transition and show that they reproduce Nekrasov's formulas for instanton counting. We also determine the asymptotic forms of the Gopakumar-Vafa invariants of the Calabi-Yau threefolds including those at higher genera from instanton amplitudes of the gauge theory.
25 pages, 5 figures; (v2) eq.(10) corrected