Some remarks on pseudo-trace functions for orbifold models associated with symplectic fermions

摘要

We propose a method to give pseudo-trace functions for vertex operator algebras satisfying Zhu's finiteness condition and apply our method to the ℤ2-orbifold model associated with d-pairs of symplectic fermions. Pseudo-trace functions are defined by using symmetric linear functions on (higher) Zhu's algebras. But our approach does not use such algebras. For d = 1, we determine the dimension of the space of one-point functions, that is, the one of the triplet mathcal{W}(2)-algebra. For d > 1, we construct 2 ~(2d-1) + 3 linearly independent one-point functions and study their values at the vacuum vector.