S3-permutation orbifolds of Virasoro vertex algebras

Abstract

In this paper, a continuation of [24], we investigate the S3-orbifold subalgebra of (Vc)⊗3, that is, we consider the S3-fixed point vertex subalgebra of the tensor product of three copies of the universal Virasoro vertex operator algebras Vc. Our main result is construction of a minimal, strong set of generators of this subalgebra for any generic values of c. More precisely, we show that this vertex algebra is of type (2,4,62,82,9,102,11,123).We also investigate two prominent examples of simple S3-orbifold algebras corresponding to central charges c=12 (Ising model) and c=−225 (i.e. (2,5)-minimal model). We prove that the former is a new unitary W-algebra of type (2,4,6,8) and the latter is isomorphic to the affine simple W-algebra of type G2 at non-admissible level −196. We also provide another version of this isomorphism using the affine W-algebra of type G2 coming from a subregular nilpotent element.