Simple current extensions of tensor products of vertex operator algebras

Hiromichi Yamada, Hiroshi Yamauchi

Published 2018-04-23Version 1

We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current extension and the fusion rule for a tensor factor. In some special case, we construct a chain of simple current extensions. As an example, we obtain a chain of simple current extensions starting from the simple affine vertex operator algebra associated with $\widehat{sl}_2$ at level a positive integer $k$. The irreducible modules are classified and the fusion rules are determined for those simple current extensions.