Boundary vertex algebras for 3d N=4 rank-0 SCFTs

We initiate the study of boundary Vertex Operator Algebras (VOAs) of topologically twisted 3d N=4 𝒩=4 rank-0 SCFTs. This is a recently introduced class of N=4 𝒩=4 SCFTs that by definition have zero-dimensional Higgs and Coulomb branches. We briefly explain why it is reasonable 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 N=2 𝒩=2 Lagrangian theory, we propose a technique for the explicit construction of its topological twists and boundary VOAs based on deformations of the holomorphic-topological twist of the N=2 𝒩=2 microscopic description. We apply this technique to the B B twist of a newly discovered family of 3d N=4 𝒩=4 rank-0 SCFTs Tᵣ 𝒯r and argue that they admit the simple affine VOAs Lᵣ (osp (1|2) ) Lr (𝔬𝔰𝔭 (1|2) ) at their boundary. In the simplest case, this leads to a novel level-rank duality between L₁ (osp (1|2) ) L1 (𝔬𝔰𝔭 (1|2) ) and the minimal model M (2, 5) M (2, 5). As an aside, we present a TQFT obtained by twisting a 3d N=2 𝒩=2 QFT that admits the M (3, 4) M (3, 4) minimal model as a boundary VOA and briefly comment on the classical freeness of VOAs at the boundary of 3d TQFTs.