Abstract
We begin by reviewing Zhu’s theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we call ‘odd trace functions’. We examine the case of the N = 1 superconformal algebra. In particular we compute an odd trace function in two different ways, and thereby obtain a new representation theoretic interpretation of a well known classical identity due to Jacobi concerning the Dedekind eta function.
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Notes
- 1.
1 The precise definition of the action involves choices of roots of unity in general. See [15] for details.
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van Ekeren, J. (2014). Vertex operator superalgebras and odd trace functions. In: Gorelik, M., Papi, P. (eds) Advances in Lie Superalgebras. Springer INdAM Series, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02952-8_13
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DOI: https://doi.org/10.1007/978-3-319-02952-8_13
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