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Modularity in Orbifold Theory for Vertex Operator Superalgebras

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Abstract

This paper is about the orbifold theory for vertex operator superalgebras. Given a vertex operator superalgebra V and a finite automorphism group G of V, we show that the trace functions associated to the twisted sectors are holomorphic in the upper half plane for any commuting pairs in G under the C2-cofinite condition. We also establish that these functions afford a representation of the full modular group if V is C2-cofinite and g-rational for any g ∈ G.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Santa Cruz, CA, 95064, USA

    Chongying Dong & Zhongping Zhao

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  1. Chongying Dong
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  2. Zhongping Zhao
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Additional information

Communicated by Y. Kawahigashi

Supported by NSF grants, China NSF grant 10328102 and a Faculty research grant from the University of California at Santa Cruz

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Dong, C., Zhao, Z. Modularity in Orbifold Theory for Vertex Operator Superalgebras. Commun. Math. Phys. 260, 227–256 (2005). https://doi.org/10.1007/s00220-005-1418-2

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  • DOI: https://doi.org/10.1007/s00220-005-1418-2

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