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

Ralph Blumenhagen·Andreas Wisskirchen
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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.

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Ralph Blumenhagen, Andreas Wisskirchen. 1994-08-15. Extension of the N=2 Virasoro algebra by two primary fields of dimension 2 and 3. https://doi.org/10.1016/0370-2693(94)01433-d

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