エキゾチックな対称性を持つ理論の存在を示唆する解析的・数値的証拠を発見 〜Haagerup対称性の謎に新たな手がかり〜

2026-03-17 九州大学

図　(E8)_1 からHaagerup対称性へ：Haagerup対称性を持つ共形場理論の存在を示唆する解析的・数値的証拠を得た。

＜関連情報＞

• https://www.kyushu-u.ac.jp/ja/researches/view/1438
• chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.kyushu-u.ac.jp/f/65084/26_0317_01.pdf
• https://journals.aps.org/prl/abstract/10.1103/6tzz-tvp7

ハーゲルップ対称性 (8)1？ Haagerup Symmetry in (8)1?

Jan Albert, Yamato Honda, Justin Kaidi, and Yunqin Zheng
Physical Review Letters  Published: 2 March, 2026
DOI: https://doi.org/10.1103/6tzz-tvp7

Abstract

We suggest that the chiral (e8)₁ theory—in many senses the simplest vertex operator algebra—may have
Haagerup symmetry H_i for i ＝ 1, 2, 3. Likewise, we suggest that the nonchiral (E₈)₁ Wess-Zumino-Witten
model may have H_i × H^op_i symmetry, and that gauging the diagonal symmetry gives a c＝ 8 theory with
Z(H₃) symmetry, which is the theory predicted in Evans and Gannon [Commun. Math. Phys. 307, 463
(2011)]. Along the way, we show that (E₈)₁ also has a Fib × Fib^op symmetry, and that gauging the diagonal
symmetry gives the (G₂)₁ × (F₄)₁ Wess-Zumino-Witten model, explaining the well-known conformal
embedding (G₂)₁ × (F₄₎₁ ⊂ (E₈)₁. Finally, we suggest a relation to theories with H3 symmetry at c ＝ 2,
6, complimenting the discussion with new modular bootstrap results.