## Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

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2007##### Author

Mason, Geoffrey

Tuite, Michael P.

Zuevsky, Alexander

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Geoffrey Mason, Michael P. Tuite and Alexander Zuevsky(2007)Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds, Geoffrey Mason, Michael P. Tuite and Alexander Zuevsky

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##### Abstract

We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, we obtain all orbifold n-point functions for a twisted module associated with a continuous automorphism generated by a Heisenberg bosonic state. The modular properties of these orbifold n-point functions are given and we describe a generalization of Fay's trisecant identity for elliptic functions.