Dualities in 4D Theories with Product Gauge Groups from Brane Configurations

TL;DR

The paper tackles nonperturbative dualities for 4D $N=1$ theories with product gauge groups $SO(N_{c1})×Sp(N_{c2})$ using brane configurations in type II string theory. By manipulating brane positions and accounting for orientifold effects, it derives a magnetic dual with ranks $\tilde{N}_{c1}$ and $\tilde{N}_{c2}$ given by $\tilde{N}_{c1}=4N_{f2}+2N_{f1}-2N_{c2}$ and $\tilde{N}_{c2}=2N_{f1}+N_{f2}-N_{c1}/2$, including a bifundamental field $X$ and a truncated quartic superpotential that constrains the chiral ring. The construction extends to alternating products of SO and Sp groups, clarifying behaviors for even versus odd numbers of factors and the corresponding D4-brane creation/annihilation required for smooth transitions, and remains consistent under a sign flip of the orientifold projection. These brane-based dualities broaden Seiberg-like dualities beyond unitary groups and motivate cross-checks with geometric singularity approaches and further field-theoretic verification.

Abstract

We study brane configurations which correspond to N=1 field theories in four dimensions. By inverting the order of the NS 5-branes and D6-branes, a check on dualities in four dimensional theories can be made. We consider a brane configuration which yields electric/magnetic duality for gauge theories with $SO(N_{c1})\times Sp(N_{c2})$ product gauge group. We also discuss the possible extension to any alternating product of SO and Sp groups. The new features arising from the intersection of the NS 5-branes on the orientifold play a crucial role in our construction.