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On the Structure of Framed Vertex Operator Algebras and Their Pointwise Frame Stabilizers

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Abstract

In this paper, we study the structure of a general framed vertex operator algebra (VOA). We show that the structure codes (C,D) of a framed VOA V satisfy certain duality conditions. As a consequence, we prove that every framed VOA is a simple current extension of the associated binary code VOA V C . This result suggests the feasibility of classifying framed vertex operator algebras, at least if the central charge is small. In addition, the pointwise frame stabilizer of V is studied. We completely determine all automorphisms in the pointwise stabilizer, which are of order 1, 2 or 4. The 4A-twisted sector and the 4A-twisted orbifold theory of the famous moonshine VOA \(V^\natural\) are also constructed explicitly. We verify that the top module of this twisted sector is of dimension 1 and of weight 3/4 and the VOA obtained by 4A-twisted orbifold construction of \(V^\natural\) is isomorphic to \(V^\natural\) itself.

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Authors and Affiliations

  1. Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan

    Ching Hung Lam

  2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Hiroshi Yamauchi

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  1. Ching Hung Lam
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  2. Hiroshi Yamauchi
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Correspondence to Hiroshi Yamauchi.

Additional information

Communicated by Y. Kawahigashi

Dedicated to Professor Koichiro Harada on his 65th birthday

Partially supported by NSC grant 94-2115-M-006-001 of Taiwan, R.O.C.

Supported by JSPS Research Fellowships for Young Scientists.

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Lam, C.H., Yamauchi, H. On the Structure of Framed Vertex Operator Algebras and Their Pointwise Frame Stabilizers. Commun. Math. Phys. 277, 237–285 (2008). https://doi.org/10.1007/s00220-007-0323-2

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  • DOI: https://doi.org/10.1007/s00220-007-0323-2

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