Permutation orbifolds of 𝔰𝔩2 vertex operator algebras

Abstract

We analyze two types of permutation orbifolds: (i) S2-orbifolds of the universal level k vertex operator algebra Vk(𝔰𝔩2) and of its simple quotient Lk(𝔰𝔩2), and (ii) the S3-orbifold of the level one simple vertex operator algebra L1(𝔰𝔩2). We determine their structures and discuss related W-algebras.