S 2-orbifolds of N = 1 and N = 2 superconformal vertex algebras and W-algebras

Abstract

We study S 2-orbifolds of N = 1 and N = 2 superconformal vertex algebras. For generic values of the central charge, we determine types of these orbifolds and prove that they are W-algebras. For some special rational values of the central charge, we get new examples of rational N = 1 vertex superalgebras. We also investigate S 2-orbifold of the Heisenberg–Virasoro vertex algebra.