Simple current extensions of vertex operator algebras by unitary modules

TL;DR

This paper establishes conditions for unitarity in vertex operator superalgebras, proves an analogue of the spin-statistics theorem, and demonstrates the existence of vertex operator algebra structures on sums of simple current modules.

Contribution

It introduces new criteria for unitarity, extends the spin-statistics theorem to conformal field theory, and constructs VOA structures from simple current modules.

Findings

Identified conditions for unitarity in vertex operator superalgebras

Proved an analogue of the conformal spin-statistics theorem

Established VOA structures on sums of simple current modules

Abstract

In this paper, a condition making vertex operator superalgebras to be unitary is determined and an analogue of conformal spin-statistics theorem in conformal field theory is proved. As an application of these results, it is proved that under some assumptions there exist vertex operator algebra structures on the direct sum of simple current unitary modules of unitary vertex operator algebras.