Torus Chiral n -Point Functions for Free Boson and Lattice Vertex Operator Algebras

Abstract

We obtain explicit expressions for all genus one chiral n-point functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions.

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

“…In particular, the partition function Z V,h (f ; τ ) and the generating function G n,h can be computed in this bosonic decomposition using the results of ref. [MT1], leading to the Jacobi triple product formula and Fay's trisecant identity (for elliptic functions) respectively. We also describe a further new generalization of Fay's trisecant identity for elliptic functions.…”

“…We may generalize these identities using Propositions 4 and 5 of [MT1] again to consider the general lattice n-point function:…”

“…This paper is one of a series devoted to the study of n-point functions for vertex operator algebras on Riemann surfaces of genus one, two and higher [T], [MT1], [MT2], [MT3]. One may define n-point functions at genus one following Zhu [Z], and use these functions together with various sewing procedures to define n-point functions at successively higher genera [T], [MT2], [MT3].…”

Tree and loop amplitudes in open twistor string theory

“…Relevant discussion is also given in [24,25]. The amplitudes can be expressed in terms of the τ -dependent invariant tensors, In what follows L 0 denotes the zero-mode generator for the Virasoro algebra associated with the current algebra.…”

Vertex Algebra Generation of Almost Holomorphic Modular Forms

“…can be reproduced via the computation of a one-point function for the Heisenberg vertex operator algebra [11,12,14]. For the Heisenberg vertex operator algebra M, the Zhu reduction gives all n-pt functions, e.g., [10,12] ( ) ( ) ( ) ( ) ( ), , ; ; ; ,…”