On Geometric Engineering of Supersymmetric Gauge Theories

Abstract

We present the basic ideas of geometric engineering of the supersymmetric quantum field theories viewed as a low energy limit of type II strings and F-theory on singular Calabi Yau manifolds. We first give the main lines of toric geometry as it is a powerful technique to deal compact complex manifolds. Then we introduce mirror symmetry which plays a crucial role in the study of superstring dualities and finally we give elements on Calabi Yau singularities. After that we study the geometric engineering of N=2 supersymmetric gauge theories in six and four dimensions. Finally we make comments regarding $N=1$ SYM in four dimensions.

Comments: 8 pages. To be published in the proceedings of the Workshop on Noncommutative Geometry, Superstrings and Particle Physics. Rabat -Morocco, (16-17 June 2000)