W-algebras as coset vertex algebras

• 成果类型: Article
• 署名作者: Arakawa, Tomoyuki; Creutzig, Thomas; Linshaw, Andrew R.
• 署名单位: Kyoto University; University of Alberta; University of Denver
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00884-3
• 发表日期: 2019
• 页码: 145-195
• 关键词: affine lie-algebras; level-rank duality; kac-moody algebras; operator-algebras; branching-rules; REPRESENTATIONS; virasoro; rationality; SPACE; characters

摘要

We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the discrete series of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Kazama-Suzuki coset vertex superalgebras is derived.