Mirror Symmetry and Level-rank Duality for 3d $\mathcal{N}=4$ Rank 0 SCFTs

Abstract

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 $W_{k-\frac{1}{2}}^{\text{min}}({\mathfrak{sp}}_{2N})$ 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.

32 pages, 1 figure; v2 completed proof of proposed level-rank duality, added/updated references. comments welcome!

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