Parafermionizing the Monster
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909033641803776 |
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| author | Honda, Yamato Kaidi, Justin Orii, Ippo |
| author_facet | Honda, Yamato Kaidi, Justin Orii, Ippo |
| contents | We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$, where $\mathcal{P}(p)$ is the theory of $\mathbb{Z}_p$-parafermions and $\mathcal{P}(p)^\vee$ is an appropriate dual theory, with global symmetry characterized by the centralizer of $\mathbb{Z}_{pA}$. By tracking the symmetries of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$ through the non-invertible gauging, we argue that the diagonal Monster CFT has $\mathrm{Rep}(\mathfrak{so}(3)_p) \boxtimes \mathrm{Rep}(\mathfrak{so}(3)_p)^\mathrm{op}$ symmetry, and hence that the holomorphic Monster theory has symmetry $\mathrm{Rep}(\mathfrak{so}(3)_p)$. We then compute the defect McKay-Thompson series associated to these symmetries, and prove that their invariance subgroups are $Γ_1(p+2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10902 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parafermionizing the Monster Honda, Yamato Kaidi, Justin Orii, Ippo High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra Representation Theory We study the parafermionization of the Monster CFT with respect to its $\mathbb{Z}_{pA}$ subgroups, with $p$ an odd prime. Under certain assumptions, we show that the parafermionization is equal to a non-invertible gauging of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$, where $\mathcal{P}(p)$ is the theory of $\mathbb{Z}_p$-parafermions and $\mathcal{P}(p)^\vee$ is an appropriate dual theory, with global symmetry characterized by the centralizer of $\mathbb{Z}_{pA}$. By tracking the symmetries of $\mathcal{P}(p) \times \mathcal{P}(p)^\vee$ through the non-invertible gauging, we argue that the diagonal Monster CFT has $\mathrm{Rep}(\mathfrak{so}(3)_p) \boxtimes \mathrm{Rep}(\mathfrak{so}(3)_p)^\mathrm{op}$ symmetry, and hence that the holomorphic Monster theory has symmetry $\mathrm{Rep}(\mathfrak{so}(3)_p)$. We then compute the defect McKay-Thompson series associated to these symmetries, and prove that their invariance subgroups are $Γ_1(p+2)$. |
| title | Parafermionizing the Monster |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2605.10902 |