Intersecting surface defects and 3d superconformal indices

We compute the 3d $$ \mathcal{N} $$ = 2 superconformal indices for 3d/1d coupled systems, which arise as the worldvolume theories of intersecting surface defects engineered by Higgsing 5d $$ \mathcal{N} $$ = 1 gauge theories. We generalize some known 3d dualities, including non-Abelian 3d mirror symmetry and 3d/3d correspondence, to some of the simple 3d/1d coupled systems. Finally we propose a q-Virasoro construction for the superconformal indices.