W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)

Abstract

We show that that the Jacobi-identities for a W-algebra with primary fields of dimensions 3, 4 and 5 allow two different solutions. The first solution can be identified with WA_4. The second is special in the sense that, even though associative for general value of the central charge, null-fields appear that violate some of the Jacobi-identities, a fact that is usually linked to exceptional W-algebras. In contrast we find for the algebra that has an additional spin 6 field only the solution WA_5.

17 pages, LaTeX, KCL-TH-92-9, DFFT-70/92

References in corpus (3)

• W-symmetry in Conformal Field Theory
• On the classification of quantum W-algebras
• Singular Contractions of W-algebras

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