Simple current extensions of vertex operator algebras by unitary 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.

I missed a condition in Theorem 2.10, which is important in this paper, hence I request to withdraw this paper