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

TL;DR

This paper constructs and analyzes extensions of the N=2 super Virasoro algebra by specific primary fields, identifying two solutions with distinct properties and implications for super W-algebras and coset models.

Contribution

It explicitly constructs two solutions extending the N=2 super Virasoro algebra with primary fields, linking one to super W_4 and proposing a unifying super W-algebra framework.

Findings

First solution identified as super W_4-algebra of CP(3) model

Second solution lacks a classical limit and is non-unitary

Self-coupling constants predicted for super W_n-algebras

Abstract

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 W_4-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 W_n-algebras. The second solution is special in the sense that it does not have a finite classical limit c->infinity and generic null fields appear. In the spirit of recent results in the N=0 case it can be understood as a unifying N=2 super W-algebra for all CP(n) coset models. It does not admit any unitary representation.