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

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.

Twisted Frobenius Identities from Vertex Operator Superalgebras

“…It is a natural generalization of results developed in [3,4]. In [1] generalizing results of [3] we obtain a closed form for the general -point function (2).…”

“…Finally, we obtain in [1] the following generalization of Proposition 15 of [4] concerning the generating properties of (8).…”

“…Since 훽푞 ⊗ 훼 = ⊗ 훼+훽 it follows that the -point function vanishes when ∑ 푖=1 푖 ̸ = 0. In [1] we describe a natural generalization of previous results in [3,4]. Firstly, consider the -point functions for highest weight vectors 1 ⊗ 훽 , which we abbreviate below to 훽 , for = 1, .…”

“…We consider in this paper the rank two free fermion vertex operator superalgebra (VOSA) = ( , Z + 1/2) ⊗2 of central charge 1 (e.g., see [4,12] for details). The weight 1/2 space is spanned by + , − with vertex operator modes which satisfy the anticommutation relations…”

Hardy Spaces on Compact Riemann Surfaces with Boundary

“…Half-order differentials play a very important role in the vertex opera-tor algebra approach to construction of partition and n-point functions for conformal field theories defined on Riemann surfaces [7][8][9]. In particular, the Szegӧ kernel [10] turned out to be key object in construction of correlation functions in free fermion conformal field theories/chiral algebras on a genus two Riemann surface sewed from two genus one Riemann surfaces [11].…”