Exceptional embeddings of $N=2$ minimal models
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arXiv
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| Format: | Preprint |
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2025
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| author | Camacho, Ana Ros Wasserman, Thomas A. |
| author_facet | Camacho, Ana Ros Wasserman, Thomas A. |
| contents | Vafa and Warner observed that the Landau-Ginzburg model associated to the potential $E_6$ (resp. $E_8$) is a product of two other models, associated to the potentials $A_2$ and $ A_3$ (resp. $A_2 $ and $ A_4$). We translate this along the Landau-Ginzburg / Conformal Field Theory correspondence to a conjecture about the unitary minimal quotients $M_d$ of the $N=2$ superconformal algebra of central charge $c_d=3-\frac{6}{d}$: there should be a conformal embedding $M_{12}\hookrightarrow M_{3} \otimes M_4$ (resp. $M_{30}\hookrightarrow M_{3} \otimes M_5$) that exhibits the product as Ostrik's $E_6$ (resp. $E_8$) algebra in the $\mathrm{Rep}(su(2)_{10})$ (resp. $\mathrm{Rep}(su(2)_{28})$) factor of the NS-sector of $\mathrm{Rep}(M_{12})$ (resp. $\mathrm{Rep}(M_{30})$). We motivate, formulate, and prove this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exceptional embeddings of $N=2$ minimal models Camacho, Ana Ros Wasserman, Thomas A. Quantum Algebra Mathematical Physics 81R10 Vafa and Warner observed that the Landau-Ginzburg model associated to the potential $E_6$ (resp. $E_8$) is a product of two other models, associated to the potentials $A_2$ and $ A_3$ (resp. $A_2 $ and $ A_4$). We translate this along the Landau-Ginzburg / Conformal Field Theory correspondence to a conjecture about the unitary minimal quotients $M_d$ of the $N=2$ superconformal algebra of central charge $c_d=3-\frac{6}{d}$: there should be a conformal embedding $M_{12}\hookrightarrow M_{3} \otimes M_4$ (resp. $M_{30}\hookrightarrow M_{3} \otimes M_5$) that exhibits the product as Ostrik's $E_6$ (resp. $E_8$) algebra in the $\mathrm{Rep}(su(2)_{10})$ (resp. $\mathrm{Rep}(su(2)_{28})$) factor of the NS-sector of $\mathrm{Rep}(M_{12})$ (resp. $\mathrm{Rep}(M_{30})$). We motivate, formulate, and prove this conjecture. |
| title | Exceptional embeddings of $N=2$ minimal models |
| topic | Quantum Algebra Mathematical Physics 81R10 |
| url | https://arxiv.org/abs/2512.10663 |