Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra
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Author(s)
van Ekeren, Jethro William
Date Issued
July 2013
Journal
Communications in Mathematical Physics
Publisher
Springer Berlin Heidelberg
Citation
Van Ekeren, Jethro. “Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra.” Communications in Mathematical Physics 322.2 (2013): 333–371.
Version
Author's final manuscript
Abstract
The purpose of this paper is to generalize Zhu’s theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover SL[subscript 2](Z)-invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain ‘odd traces’ on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional SL[subscript 2](Z)-invariant space. We close the paper with several examples.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00220-013-1758-2
