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Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
by Dongmin Gang, Heesu Kang, Seongmin Kim
Submission summary
| Authors (as registered SciPost users): | HEESU KANG |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2405.16377v3 (pdf) |
| Date submitted: | Jan. 21, 2026, 8:48 a.m. |
| Submitted by: | HEESU KANG |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Using 3D-3D correspondence, we construct 3D dual bulk field theories for general Virasoro minimal models $M(P,Q)$. These theories correspond to Seifert fiber spaces $S^2 ((P,P-R),(Q,S),(3,1))$ with two integers $(R,S)$ satisfying $PS-QR =1$. In the unitary case, where $|P-Q|=1$, the bulk theory has a mass gap and flows to a unitary topological field theory (TQFT) in the IR, which is expected to support the chiral Virasoro minimal model at the boundary under an appropriate boundary condition. For the non-unitary case, where $|P-Q|>1$, the bulk theory flows to a 3D $\mathcal{N}=4$ rank-0 superconformal field theory, whose topologically twisted theory supports the chiral minimal model at the boundary. We also provide a concrete field theory description of the 3D bulk theory using $T[SU(2)]$ theories. Our proposals are supported by various consistency checks using 3D-3D relations and direct computations of various partition functions.
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