Torus n-Point Functions for -graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds

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.