Intertwining operators and fusion rules for vertex operator algebras arising from symplectic fermions

TL;DR

This paper computes the fusion rules for a specific vertex operator algebra derived from symplectic fermions and shows its fusion algebra is isomorphic to the Klein four group, advancing understanding of its module structure.

Contribution

It explicitly determines the fusion rules for modules of the symplectic fermionic vertex operator algebra and identifies its fusion algebra as a Klein four group algebra.

Findings

Fusion rules among simple modules are explicitly determined.

Fusion algebra is isomorphic to the Klein four group algebra.

Provides a detailed structure of modules for the algebra.

Abstract

We determine fusion rules (dimensions of the space of intertwining operators) among simple modules for the vertex operator algebra obtained as an even part of the symplectic fermionic vertex operator superalgebra. By using these fusion rules we show that the fusion algebra of this vertex operator algebra is isomorphic to the group algebra of the Klein four group over Z.