Free Field Realization of Supersymmetric W-algebras

Abstract

We show that supersymmetric(SUSY) W-algebra of generic level can be realized as an intersection of the kernels of the screening operators. Applying this result to principal SUSY W-algebras, we get their free field realization inside the SUSY Heisenberg vertex algebras. Furthermore, the screening operators for principal SUSY W-algebras allow us to present them as intersections of the principal SUSY W-algebras associated with $\mathfrak{osp}(1|2)$, $\mathfrak{osp}(2|2)$, $\mathfrak{osp}(3|2)$ and $\mathfrak{osp}(4|2)$, tensored with SUSY Heisenberg vertex algebras.