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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.16377 |
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| _version_ | 1866915850734272512 |
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| author | Gang, Dongmin Kang, Heesu Kim, Seongmin |
| author_facet | Gang, Dongmin Kang, Heesu Kim, Seongmin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models Gang, Dongmin Kang, Heesu Kim, Seongmin High Energy Physics - Theory Geometric Topology 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. |
| title | Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models |
| topic | High Energy Physics - Theory Geometric Topology |
| url | https://arxiv.org/abs/2405.16377 |