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.
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Communicated by Y. Kawahigashi
Partial support provided by NSF, NSA and the Committee on Research, University of California, Santa Cruz.
Supported by a Science Foundation Ireland Frontiers of Research Grant, and by Max-Planck Institut für Mathematik, Bonn.
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Mason, G., Tuite, M.P. & Zuevsky, A. Torus n-Point Functions for \({\mathbb{R}}\) -graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds. Commun. Math. Phys. 283, 305–342 (2008). https://doi.org/10.1007/s00220-008-0510-9
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DOI: https://doi.org/10.1007/s00220-008-0510-9