Geometry, D-branes and N=1 Duality in Four Dimensions with Product Gauge Group

TL;DR

This paper explores geometric realizations of N=1 dualities in four-dimensional supersymmetric gauge theories using D6-branes on Calabi-Yau threefolds, extending to multiple product gauge groups and providing new geometric insights.

Contribution

It introduces a geometric framework for understanding N=1 dualities with product gauge groups, including new descriptions for triple and multiple gauge group configurations.

Findings

Geometric description of dualities with $SU(N_{c1})\times SU(N_{c2})$ gauge groups.

Simple geometric interpretation for triple product gauge groups.

Natural emergence of semi-infinite D4-branes as flavor groups in dual theories.

Abstract

We study N=1 dualities in four dimensional supersymmetric gauge theories by D 6-branes wrapping around 3-cycles of Calabi-Yau threefolds in the type IIA string theory. We consider the models involving $SU(N_{c1})\times SU(N_{c2})$ product gauge group without or with adjoint matter in terms of geometrical realisation of the configuration of D 6-branes wrapped 3-cycles. We also find simple geometric description for the triple product gauge group $SU(N_{c1})\times SU(N_{c2})\times SU(N_{c3})$ interpreted recently by Brodie and Hanany in the context of D brane configurations together with NS 5-branes. Their introduction of semi-infinite D 4-branes appears naturally by looking at the flavor group in the dual theory. We generalize to product of arbitrary number of gauge groups.