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タイトル: | Rationality and fusion rules of exceptional $mathcal {W}$-algebras |
著者: | Arakawa, Tomoyuki ![]() ![]() ![]() van Ekeren, Jethro |
著者名の別形: | 荒川, 知幸 |
キーワード: | Vertex algebras $mathcal {W}$-algebras fusion rules rational conformal field theory 17B69 81R10 17B67 17B3 |
発行日: | 7-Jul-2023 |
出版者: | European Mathematical Society - EMS - Publishing House GmbH |
誌名: | Journal of the European Mathematical Society |
巻: | 25 |
号: | 7 |
開始ページ: | 2763 |
終了ページ: | 2813 |
抄録: | First, we prove the Kac–Wakimoto conjecture on modular invariance of characters of exceptional affine $mathcal {W}$-algebras. In fact more generally we prove modular invariance of characters of all lisse $mathcal {W}$-algebras obtained through Hamiltonian reduction of admissible affine vertex algebras. Second, we prove the rationality of a large subclass of these $mathcal {W}$-algebras, which includes all exceptional $mathcal {W}$-algebras of type $mathcal {A}$ and lisse subregular $mathcal {W}$-algebras in simply laced types. Third, for the latter cases we compute $mathcal {S}$-matrices and fusion rules. Our results provide the first examples of rational $mathcal {W}$-algebras associated with nonprincipal distinguished nilpotent elements, and the corresponding fusion rules are rather mysterious |
著作権等: | © 2022 European Mathematical Society Published by EMS Press and licensed under a CC BY 4.0 license. |
URI: | http://hdl.handle.net/2433/285245 |
DOI(出版社版): | 10.4171/jems/1250 |
出現コレクション: | 学術雑誌掲載論文等 |
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