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

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 $W_{N}$ 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 $S^2((P,P{-}R),(Q,S),(N{+}1,-2N{-}1))$ 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 $W_N(P, Q)$, we present preliminary checks and leave further consistency checks for future work.