2002/12/31 by Amer Iqbal, Amir-Kian Kashani-Poor
Physics and Astronomy · #hep-th
published as Adv.Theor.Math.Phys. 7 (2004) 457-497 · 39 pages, references added, typos corrected, cosmetic changes
arxiv created 2004/01/02 · arxiv updated 2009/11/30
The instanton partition function of N=2, D=4 SU(2) gauge theory is obtained by taking the field theory limit of the topological open string partition function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the open string side is obtained by geometric transition from local F0 which is used in the geometric engineering of the SU(2) theory. The partition function obtained from the Chern-Simons theory agrees with the closed topological string partition function of local F0 proposed recently by Nekrasov. We also obtain the partition functions for local F1 and F2 CY3-folds and show that the topological string amplitudes of all local Hirzebruch surfaces give rise to the same field theory limit. It is shown that a generalization of the topological closed string partition function whose field theory limit is the generalization of the instanton partition function, proposed by Nekrasov, can be determined easily from the Chern-Simons theory.