## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 10, Number 1 (2006), 1-32.

### ${\rm SU}(N)$ geometries and topological string amplitudes

Amer Iqbal and Amir-Kian Kashani-Poor

#### Abstract

It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3-folds giving rise to $\mathcal{N}=2$ 4D $SU(N)$ gauge theory via geometric engineering can be obtained from gauge instanton calculus. We verify this surprising conjecture by calculating the partition functions for such local CYs using diagrammatic techniques inspired by geometric transitions. Determining the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allows us to take the field theory limit.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 10, Number 1 (2006), 1-32.

**Dates**

First available in Project Euclid: 30 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1154236236

**Mathematical Reviews number (MathSciNet)**

MR2222220

**Zentralblatt MATH identifier**

1101.81088

**Subjects**

Primary: 81T30: String and superstring theories; other extended objects (e.g., branes) [See also 83E30]

Secondary: 81T13: Yang-Mills and other gauge theories [See also 53C07, 58E15] 81T45: Topological field theories [See also 57R56, 58Dxx]

#### Citation

Iqbal, Amer; Kashani-Poor, Amir-Kian. ${\rm SU}(N)$ geometries and topological string amplitudes. Adv. Theor. Math. Phys. 10 (2006), no. 1, 1--32. https://projecteuclid.org/euclid.atmp/1154236236