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Rationality of Bershadsky-Polyakov Vertex Algebras

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Abstract

We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras \({W_3^{(2)}}\) at level k =  p/2−3 with \({p = 3, 5, 7, 9, \dots}\) . This gives new examples of rational conformal field theories.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Tomoyuki Arakawa

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  1. Tomoyuki Arakawa
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Correspondence to Tomoyuki Arakawa.

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Communicated by Y. Kawahigashi

This work is partially supported by the JSPS Grant-in-Aid for Scientific Research (B) No. 20340007.

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Arakawa, T. Rationality of Bershadsky-Polyakov Vertex Algebras. Commun. Math. Phys. 323, 627–633 (2013). https://doi.org/10.1007/s00220-013-1780-4

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  • DOI: https://doi.org/10.1007/s00220-013-1780-4

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