Haagerup Symmetry in $(E_8)_1$?
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| Format: | Preprint |
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2025
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| author | Albert, Jan Honda, Yamato Kaidi, Justin Zheng, Yunqin |
| author_facet | Albert, Jan Honda, Yamato Kaidi, Justin Zheng, Yunqin |
| contents | We suggest that the chiral $(\mathfrak{e}_8)_1$ theory -- in many senses the simplest VOA -- may have Haagerup symmetry $\mathcal{H}_i$ for $i=1,2,3$. Likewise, we suggest that the non-chiral $(E_8)_1$ WZW model may have $\mathcal{H}_i \times \mathcal{H}_i^\textrm{op}$ symmetry, and that gauging the diagonal symmetry gives a $c=8$ theory with $\mathcal{Z}(\mathcal{H}_3)$ symmetry, which is the theory predicted in \cite{Evans:2010yr}. Along the way, we show that $(E_8)_1$ also has a $\mathrm{Fib} \times \mathrm{Fib}^\text{op}$ symmetry, and that gauging the diagonal symmetry gives the $(G_2)_1 \times (F_4)_1$ WZW model, explaining the well-known conformal embedding $(G_2)_1 \times (F_4)_1 \subset (E_8)_1$. Finally, we suggest a relation to theories with $\mathcal{H}_3$ symmetry at $c=2,6$, complimenting the discussion with new modular bootstrap results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_08225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Haagerup Symmetry in $(E_8)_1$? Albert, Jan Honda, Yamato Kaidi, Justin Zheng, Yunqin High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra We suggest that the chiral $(\mathfrak{e}_8)_1$ theory -- in many senses the simplest VOA -- may have Haagerup symmetry $\mathcal{H}_i$ for $i=1,2,3$. Likewise, we suggest that the non-chiral $(E_8)_1$ WZW model may have $\mathcal{H}_i \times \mathcal{H}_i^\textrm{op}$ symmetry, and that gauging the diagonal symmetry gives a $c=8$ theory with $\mathcal{Z}(\mathcal{H}_3)$ symmetry, which is the theory predicted in \cite{Evans:2010yr}. Along the way, we show that $(E_8)_1$ also has a $\mathrm{Fib} \times \mathrm{Fib}^\text{op}$ symmetry, and that gauging the diagonal symmetry gives the $(G_2)_1 \times (F_4)_1$ WZW model, explaining the well-known conformal embedding $(G_2)_1 \times (F_4)_1 \subset (E_8)_1$. Finally, we suggest a relation to theories with $\mathcal{H}_3$ symmetry at $c=2,6$, complimenting the discussion with new modular bootstrap results. |
| title | Haagerup Symmetry in $(E_8)_1$? |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2512.08225 |