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Orbifold Construction of Holomorphic Vertex Operator Algebras Associated to Inner Automorphisms

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Abstract

In this article, we construct three new holomorphic vertex operator algebras of central charge 24 using the \({\mathbb{Z}_{2}}\)-orbifold construction associated to inner automorphisms. Their weight one subspaces have the Lie algebra structures D 7,3 A 3,1 G 2,1, E 7,3 A 5,1, and \({A_{8,3}A_{2,1}^2}\). In addition, we discuss the constructions of holomorphic vertex operator algebras with Lie algebras A 5,6 C 2,3 A 1,2 and \({D_{6,5}A_{1,1}^2}\) from holomorphic vertex operator algebras with Lie algebras C 5,3 G 2,2 A 1,1 and \({A_{4,5}^2}\), respectively.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan

    Ching Hung Lam

  2. National Center for Theoretical Sciences of Taiwan, Taipei, Taiwan

    Ching Hung Lam

  3. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Hiroki Shimakura

Authors
  1. Ching Hung Lam
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  2. Hiroki Shimakura
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Correspondence to Ching Hung Lam.

Additional information

Communicated by Y. Kawahigashi

C. H. Lam was partially supported by NSC Grant 100-2628-M-001005-MY4 of Taiwan. H. Shimakura was partially supported by JSPS KAKENHI Grant Numbers 23540013 and 26800001, and by Grant for Basic Science Research Projects from The Sumitomo Foundation.

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Lam, C.H., Shimakura, H. Orbifold Construction of Holomorphic Vertex Operator Algebras Associated to Inner Automorphisms. Commun. Math. Phys. 342, 803–841 (2016). https://doi.org/10.1007/s00220-015-2484-8

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  • DOI: https://doi.org/10.1007/s00220-015-2484-8

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