Seiberg-Witten Geometry with Various Matter Contents

TL;DR

This paper derives the Seiberg-Witten geometries for various N=2 gauge theories with different matter contents, using gauge symmetry breaking and geometric methods, and confirms results through multiple approaches.

Contribution

It provides explicit Seiberg-Witten solutions for SO(2N_c) and SU(N_c) gauge theories with diverse matter hypermultiplets, connecting geometric engineering and superpotential methods.

Findings

Derived Seiberg-Witten geometries for SO(2N_c) with matter.

Compared geometric engineering results with brane dynamics.

Reproduced results using N=1 confining phase superpotentials.

Abstract

We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with massive fundamental hypermultiplets. In a similar way the Seiberg-Witten geometry is determined for N=2 SU(N_c) (N_c \leq 6) gauge theory with massive antisymmetric and fundamental hypermultiplets. Whenever possible we compare our results expressed in the form of ALE fibrations with those obtained by geometric engineering and brane dynamics, and find a remarkable agreement. We also show that these results are reproduced by using N=1 confining phase superpotentials.