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We initiate the study of boundary Vertex Operator Algebras (VOAs) oftopologically twisted 3d $\mathcal{N}=4$ rank-0 SCFTs. This is a recentlyintroduced class of $\mathcal{N}=4$ SCFTs that by definition havezero-dimensional Higgs and Coulomb branches. We briefly explain why it isreasonable to obtain rational VOAs at the boundary of their topological twists.When a rank-0 SCFT is realized as the IR fixed point of a $\mathcal{N}=2$Lagrangian theory, we propose a technique for the explicit construction of itstopological twists and boundary VOAs based on deformations of theholomorphic-topological twist of the $\mathcal{N}=2$ microscopic description.We apply this technique to the $B$ twist of a newly discovered family of 3d$\mathcal{N}=4$ rank-0 SCFTs ${\mathcal T}_r$ and argue that they admit thesimple affine VOAs $L_r(\mathfrak{osp}(1|2))$ at their boundary. In thesimplest case, this leads to a novel level-rank duality between$L_1(\mathfrak{osp}(1|2))$ and the minimal model $M(2,5)$. As an aside, wepresent a TQFT obtained by twisting a 3d $\mathcal{N}=2$ QFT that admits the$M(3,4)$ minimal model as a boundary VOA and briefly comment on the classicalfreeness of VOAs at the boundary of 3d TQFTs.

Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs