Branes, Geometry and N=1 Duality with Product Gauge Groups of SO and Sp

TL;DR

This paper explores new N=1 dualities in four-dimensional supersymmetric gauge theories with product gauge groups of SO and Sp, using brane configurations and geometric methods in type IIA string theory.

Contribution

It generalizes previous dualities to more complex product gauge groups and introduces a method to obtain these dualities by reversing brane orderings.

Findings

Conjectured dualities for multiple product gauge groups.

Dualities derived by reversing NS5 and D6 brane orderings.

Described dualities using Calabi-Yau threefolds in type IIA string theory.

Abstract

We study N=1 dualities in four dimensional supersymmetric gauge theories as the worldvolume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_{c1}) x Sp(N_{c2}) with the superpotential W=Tr X^4 to the case of W= Tr X^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_{c1}) x Sp(N_{c2}) x SO(N_{c3}), SO(N_{c1}) x Sp(N_{c2}) x SO(N_{c3}) x Sp(N_{c4}) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3 cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.