Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra
Author(s)van Ekeren, Jethro William
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Mathematical Physics
Springer Berlin Heidelberg
Van Ekeren, Jethro. “Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra.” Communications in Mathematical Physics 322.2 (2013): 333–371.
Author's final manuscript