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

TL;DR

This paper introduces a family of 3d N=4 superconformal field theories with trivial Coulomb and Higgs branches, proposing new connections between vertex operator algebras, modular tensor categories, and a novel level-rank duality.

Contribution

It proposes a new class of 3d N=4 SCFTs with zero-dimensional moduli spaces and links their line operator categories to specific vertex operator algebras, revealing a novel level-rank duality.

Findings

Identification of vertex operator algebras modeling line operator categories

Proposal of a new level-rank duality related to mirror symmetry

Conjectural q-series identities of mathematical interest

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