Extension of the N = 2 Virasoro algebra by two primary fields of dimension 2 and 3

We explicitly construct the extension of the N = 2 super Virasoro algebra by two super primary fields of dimension two and three with vanishing u(1)-charge. Using a super covariant formalism we obtain two different solutions both consistent for generic values of the central charge c. The first one can be identified with the super W4-algebra — the symmetry algebra of the CP(3) Kazama-Suzuki model. With the help of unitarity arguments we predict the self-coupling constant of the field of dimension two for all super Wn-algebras. The second solution is special in the sense that it does not have a finite classical limit c → ∞ and generic null fields appear. In the spirit of recent results in the N = 0 case this can be understood as a unifying N = 2 super W-algebra for all CP (n) coset models. It does not admit any unitary representation.