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

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.