TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.057
TI  - Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
PY  - 2024/08/16
UR  - https://scipost.org/SciPostPhys.17.2.057
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 057
A1  - Ferrari, Andrea E. V.
AU  - Garner, Niklas
AU  - Kim, Heeyeon
AB  - We initiate the study of boundary Vertex Operator Algebras (VOAs) of topologically twisted 3d $\mathcal{N}=4$ rank-0 SCFTs. This is a recently introduced class of $\mathcal{N}=4$ 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 $\mathcal{N}=2$ 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 $\mathcal{N}=2$ 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 the simple affine VOAs $L_r(\mathfrak{osp}(1|2))$ at their boundary. In the simplest case, this leads to a novel level-rank duality between $L_1(\mathfrak{osp}(1|2))$ and the minimal model $M(2,5)$. As an aside, we present 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 classical freeness of VOAs at the boundary of 3d TQFTs.
ER  -

@Article{10.21468/SciPostPhys.17.2.057,
	title={{Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs}},
	author={Andrea E. V. Ferrari and Niklas Garner and Heeyeon Kim},
	journal={SciPost Phys.},
	volume={17},
	pages={057},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.057},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.057},
}