  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 F_0 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 F_0 proposed recently by Nekrasov. We also obtain
the partition functions for local F_1 and F_2 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.

High Energy Physics - Theory