  We introduce a family of 3d $\mathcal{N} = 4$ superconformal field theories
that have zero-dimensional Coulomb and Higgs branches and propose that the
rational vertex operator algebras $W^{\text{min}}_{k -
\scriptstyle{\frac{1}{2}}}(\mathfrak{sp}_{2N})$ and
$L_{k}(\mathfrak{osp}_{1|2N})$ model the modular tensor categories of line
operators in their topological $A$ and $B$ twists, respectively. Our analysis
indicates that the action of 3d mirror symmetry on this family of theories is
related to a novel level-rank duality and leads to several conjectural
$q$-series identities of independent interest.
