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

Abstract

We initiate the study of boundary Vertex Operator Algebras (VOAs) of topologically twisted 3d \mathcal{N}=4𝒩=4 rank-0 SCFTs. This is a recently introduced class of \mathcal{N}=4𝒩=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 \mathcal{N}=2𝒩=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 \mathcal{N}=2𝒩=2 microscopic description. We apply this technique to the BB twist of a newly discovered family of 3d \mathcal{N}=4𝒩=4 rank-0 SCFTs {\mathcal T}_r𝒯r and argue that they admit the simple affine VOAs L_r(\mathfrak{osp}(1|2))Lr(𝔬𝔰𝔭(1|2)) at their boundary. In the simplest case, this leads to a novel level-rank duality between L_1(\mathfrak{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 \mathcal{N}=2𝒩=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.