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Modularity of trace functions in orbifold theory for Z-graded vertex operator superalgebras

Chongying Dong·Zhongping Zhao
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Abstract

We study the trace functions in orbiford theory for Z-graded vertex operator superalgebras and obtain a modular invariance result. More precisely, let V be a C_2-cofinite Z-graded vertex operator superalgebra and G a finite automorphism group of V. Then for any commuting pairs (g,h) in G, the hσ-trace functions associated to the simple g-twisted V-modules are holomorphic in the upper half plane where σis the canonical involution on V coming from the superspace structure of V. If V is further g-rational for every g n G, the trace unctions afford a representation for the full modular group SL(2,Z).

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Chongying Dong, Zhongping Zhao. 2006-01-23. Modularity of trace functions in orbifold theory for Z-graded vertex operator superalgebras. https://arxiv.org/abs/math/0601571

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