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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.23122 |
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| _version_ | 1866912793544884224 |
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| author | Gang, Dongmin Park, Byoungyoon Sohn, Huijoon |
| author_facet | Gang, Dongmin Park, Byoungyoon Sohn, Huijoon |
| contents | In 2003, Hikami and Kirillov uncovered an intriguing connection between torus knots $\mathcal{K}_{(P,Q)}$ and Virasoro minimal models $\mathcal{M}(P,Q)$ by relating the Kashaev invariants of the knots to the characters of the corresponding minimal models. In this work, we recover and extend this connection by combining the 3D--3D correspondence with a bulk--boundary correspondence. More concretely, we study the 3D $\mathcal{N}=2$ gauge theories associated with torus-knot complements via the Dimofte--Gaiotto--Gukov construction and show that, in the infrared, these theories either flow to a unitary TQFT (when $|P-Q| = 1$), whose boundary chiral algebra reproduces that of the associated unitary minimal model, or to a 3D $\mathcal{N}=4$ rank-0 SCFT (when $|P-Q| > 1$), which realizes the corresponding non-unitary chiral minimal model at the boundary after an appropriate topological twist. This framework yields new Nahm-sum-like expressions for the characters of Virasoro minimal models and other related rational conformal field theories, providing a systematic algorithm for constructing characters of rational VOAs directly from the combinatorial data of an ideal triangulation of a non-hyperbolic knot complement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torus Knots and Minimal Models Revisited : Rational VOA characters from non-hyperbolic knots Gang, Dongmin Park, Byoungyoon Sohn, Huijoon High Energy Physics - Theory Geometric Topology Number Theory In 2003, Hikami and Kirillov uncovered an intriguing connection between torus knots $\mathcal{K}_{(P,Q)}$ and Virasoro minimal models $\mathcal{M}(P,Q)$ by relating the Kashaev invariants of the knots to the characters of the corresponding minimal models. In this work, we recover and extend this connection by combining the 3D--3D correspondence with a bulk--boundary correspondence. More concretely, we study the 3D $\mathcal{N}=2$ gauge theories associated with torus-knot complements via the Dimofte--Gaiotto--Gukov construction and show that, in the infrared, these theories either flow to a unitary TQFT (when $|P-Q| = 1$), whose boundary chiral algebra reproduces that of the associated unitary minimal model, or to a 3D $\mathcal{N}=4$ rank-0 SCFT (when $|P-Q| > 1$), which realizes the corresponding non-unitary chiral minimal model at the boundary after an appropriate topological twist. This framework yields new Nahm-sum-like expressions for the characters of Virasoro minimal models and other related rational conformal field theories, providing a systematic algorithm for constructing characters of rational VOAs directly from the combinatorial data of an ideal triangulation of a non-hyperbolic knot complement. |
| title | Torus Knots and Minimal Models Revisited : Rational VOA characters from non-hyperbolic knots |
| topic | High Energy Physics - Theory Geometric Topology Number Theory |
| url | https://arxiv.org/abs/2512.23122 |