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arXiv · 2406.00138

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

Thomas Creutzig·Niklas Garner·Heeyeon Kim
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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.

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Thomas Creutzig, Niklas Garner, Heeyeon Kim. 2024-05-31. Mirror Symmetry and Level-rank Duality for 3d $\mathcal{N} = 4$ Rank 0 SCFTs. https://arxiv.org/abs/2406.00138

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