Elliptic Fibrations and Elliptic Models

TL;DR

This paper investigates the geometric structure of Seiberg-Witten curves in N=2 supersymmetric gauge theories derived from string theory, focusing on elliptic fibrations and their singularities in M-theory models.

Contribution

It provides a detailed description of the M-theory background as an elliptic fibration and formulates the Seiberg-Witten curves within this geometric framework.

Findings

Explicit elliptic fibration models for the theories studied

Characterization of singularities in the elliptic surfaces

Representation of Seiberg-Witten curves as subvarieties

Abstract

We study the Seiberg-Witten curves for N=2 SUSY gauge theories arising from type IIA string configurations with two orientifold sixplanes. Such theories lift to elliptic models in M-theory. We express the M-theory background for these models as a nontrivial elliptic fibration over C. We discuss singularities of this surface, and write the Seiberg-Witten curve for several theories as a subvariety of this surface.