Non-hyperbolic 3-manifolds and bulk field theories for supersymmetric/WN minimal models

A bstract Building on the work of Gang, Kang, and Kim [ arXiv:2405.16377 ], we propose 3D bulk dual field theories for 2D $$ \mathcal{N}=1 $$ N = 1 supersymmetric minimal models SM ( P , Q ) and W N algebra minimal models W N ( P , Q ). We associate to SM ( P , Q ) a Seifert fibered space S 2 (( P , P − R ), ( Q , S ), (3, 1)) with PS − QR = 2, and for W N ( P , Q ) a Seifert fibered space S 2 (( P , P − R ), ( Q , S ), ( N +1, −2 N − 1)) with PS − QR = 1, and realize the bulk theory via the 3D-3D correspondence. For the unitary series, the bulk theory flows in the IR to a gapped phase which, under suitable boundary conditions, supports the unitary chiral minimal model on the boundary. For the non-unitary series, the bulk theory flows to the 3D $$ \mathcal{N}=4 $$ N = 4 superconformal field theory whose topological twist yields a non-unitary topological field theory supporting the non-unitary chiral minimal model on the boundary under appropriate boundary conditions. We also propose UV gauge theory descriptions of the bulk theories obtained by gluing T [SU( n )] building blocks. For SM ( P , Q ), we provide non-trivial consistency checks — matching between various bulk partition functions and boundary conformal data — while for W N ( P , Q ), we present preliminary checks and leave further consistency checks for future work.