Building on the work of Gang, Kang, and Kim [arXiv:2405.16377], we propose 3D bulk dual field theories for 2D \( \mathcal{N}=1 \) supersymmetric minimal models SM(P, Q) and WN algebra minimal models WN(P, Q). We associate to SM(P, Q) a Seifert fibered space S2((P, P − R), (Q, S), (3, 1)) with PS − QR = 2, and for WN(P, Q) a Seifert fibered space S2((P, P − R), (Q, S), (N+1, −2N − 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 \( \mathcal{N}=4 \) 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 WN(P, Q), we present preliminary checks and leave further consistency checks for future work.
