Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

Details Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

2011-11-02

arxiv.org/abs/1111.0682v2

Mathematics

Representation Theory

39 pages, references corrected

Scientific paper

The purpose of this paper is to generalize Zhu's theorem about characters of modules over a vertex operator algebra to the setting of a vertex operator superalgebra whose vectors may have rational, rather than integer, conformal weights. It turns out that to recover SL(2, Z)-invariance of the characters, it is necessary to include twisted modules into the discussion. Another new feature arises in the super-case; the space of conformal blocks is no longer spanned by the trace functions of Zhu, the twisted trace functions of Dong, Li and Mason, and their super-analogues. Some `nonstandard' supertrace functions must be included. We prove that the space of supertrace functions, thus supplemented, spans a finite dimensional SL(2, Z)-invariant space. We close the paper with several examples.

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