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

TL;DR

This paper computes genus one n-point functions for real-graded vertex operator superalgebras, including orbifold functions for twisted modules, and explores their modular properties and generalizations of Fay's identity.

Contribution

It provides explicit calculations of n-point functions for rank one and two fermion VOAs, including orbifold functions for continuous automorphisms, and analyzes their modular behavior.

Findings

Explicit n-point functions for rank one and two fermion VOAs.

Orbifold n-point functions for twisted modules under continuous automorphisms.

Modular properties and a generalized Fay's trisecant identity.

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.