4D/3D reduction of dualities: mirrors on the circle

We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a confining sector, giving a unified mechanism for the brane reduction of dualities.