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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.23664 |
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| _version_ | 1866918439277297664 |
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| author | Antunes, António Suchel, Noé |
| author_facet | Antunes, António Suchel, Noé |
| contents | Fixed points of $N$ coupled Virasoro minimal models have recently been argued to provide large classes of compact unitary CFTs with $c>1$ and only Virasoro chiral symmetry. In this paper, we vastly increase the set of such potential irrational fixed points by considering couplings that break the maximal $G=S_N$ symmetry into various subgroups $H\subset G$. We rigorously classify all the fixed points with $N=4,5$ and do an extensive search for solutions of the beta function equations with $N\geq6$. In particular, we find non-trivial fixed points with $H=\mathbb{Z}_{N-1} \rtimes \mathbb{Z}_2, \, S_{M}\times S_{N-M}$ and rigorously prove that real fixed points with $H=(S_{N/2}\times S_{N/2})\rtimes \mathbb{Z}_2$ exist for all even $N\geq6$. We also identify fixed points with finite Lie-type symmetry $H=\rm{PSL}_2(N)\subset S_N$ where $N=7,11,13$ and uncover a non-unitary fixed point with $H=M_{22}\subset S_{22}$, a sporadic Mathieu group. Along the way, we encounter conformal manifolds at leading order in perturbation theory which we resolve at sub-leading order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Taxonomy of coupled minimal models from finite groups Antunes, António Suchel, Noé High Energy Physics - Theory Fixed points of $N$ coupled Virasoro minimal models have recently been argued to provide large classes of compact unitary CFTs with $c>1$ and only Virasoro chiral symmetry. In this paper, we vastly increase the set of such potential irrational fixed points by considering couplings that break the maximal $G=S_N$ symmetry into various subgroups $H\subset G$. We rigorously classify all the fixed points with $N=4,5$ and do an extensive search for solutions of the beta function equations with $N\geq6$. In particular, we find non-trivial fixed points with $H=\mathbb{Z}_{N-1} \rtimes \mathbb{Z}_2, \, S_{M}\times S_{N-M}$ and rigorously prove that real fixed points with $H=(S_{N/2}\times S_{N/2})\rtimes \mathbb{Z}_2$ exist for all even $N\geq6$. We also identify fixed points with finite Lie-type symmetry $H=\rm{PSL}_2(N)\subset S_N$ where $N=7,11,13$ and uncover a non-unitary fixed point with $H=M_{22}\subset S_{22}$, a sporadic Mathieu group. Along the way, we encounter conformal manifolds at leading order in perturbation theory which we resolve at sub-leading order. |
| title | Taxonomy of coupled minimal models from finite groups |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.23664 |