On Geometric Engineering of Supersymmetric Gauge Theories

TL;DR

This paper explores how supersymmetric gauge theories can be constructed using geometric methods involving Calabi-Yau manifolds, mirror symmetry, and string dualities, providing a framework for understanding their low-energy limits.

Contribution

It introduces a comprehensive geometric approach to engineering supersymmetric gauge theories from string theory compactifications, emphasizing toric geometry and Calabi-Yau singularities.

Findings

Demonstrates the use of toric geometry in modeling complex manifolds.

Shows how mirror symmetry aids in studying superstring dualities.

Discusses geometric engineering of N=2 supersymmetric theories in various dimensions.

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.