## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 7, Number 3 (2003), 457-497.

### Instanton Counting and Chern-Simons Theory

Amer Iqbal and Amir-Kian Kashani-Poor

#### Abstract

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 *IP*^{1} X *IP*^{1} 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 *IP*^{1} X *IP*^{1}
proposed recently by Nekrasov. We also obtain the
partition functions for local *IF*^{1} and *IF*^{2} CY3-folds and
show that the topological string amplitudes of all three 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.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 7, Number 3 (2003), 457-497.

**Dates**

First available in Project Euclid: 4 April 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1112627375

**Mathematical Reviews number (MathSciNet)**

MR2030057

**Zentralblatt MATH identifier**

1044.32022

#### Citation

Iqbal, Amer; Kashani-Poor, Amir-Kian. Instanton Counting and Chern-Simons Theory. Adv. Theor. Math. Phys. 7 (2003), no. 3, 457--497. https://projecteuclid.org/euclid.atmp/1112627375