  We consider 5d supersymmetric gauge theories with unitary groups in the
$\Omega$-background and study codim-2/4 BPS defects supported on orthogonal
planes intersecting at the origin along a circle. The intersecting defects
arise upon implementing the most generic Higgsing (geometric transition) to the
parent higher dimensional theory, and they are described by pairs of 3d
supersymmetric gauge theories with unitary groups interacting through 1d matter
at the intersection. We explore the relations between instanton and generalized
vortex calculus, pointing out a duality between intersecting defects subject to
the $\Omega$-background and a deformation of supergroup gauge theories, the
exact supergroup point being achieved in the self-dual or unrefined limit.
Embedding our setup into refined topological strings and in the simplest case
when the parent 5d theory is Abelian, we are able to identify the supergroup
theory dual to the intersecting defects as the supergroup version of refined
Chern-Simons theory via open/closed duality. We also discuss the BPS/CFT side
of the correspondence, finding an interesting large rank duality with
super-instanton counting.
