Geometry, D-Branes and N=1 Duality in Four Dimensions I

TL;DR

This paper explores N=1 dualities in 4D supersymmetric gauge theories through a geometric approach involving D6-branes wrapped on 3-cycles in Calabi-Yau threefolds, extending previous models to include various gauge groups.

Contribution

It provides a new geometric framework for understanding N=1 dualities in 4D gauge theories, including SU, SO, and Sp groups, by relating them to D6-brane configurations in string theory.

Findings

Geometrical description of electric-magnetic duality via D6-brane configurations.

Extension of previous models to include additional gauge groups and fields.

Simplified visualization of dualities in terms of wrapped branes.

Abstract

We consider N=1 dualities in four dimensional supersymmetric gauge theories as a geometrical realization of wrapping D 6-branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. By extending the recent work of Ooguri and Vafa to the case of $SU, SO and Sp$ gauge groups with additional fields together with defining fields, we give simple geometrical descriptions of the interrelation between the electric theory and its magnetic dual in terms of the configuration of D 6-branes wrapped 3-cycles.