W-Algebras, New Rational Models and Completeness of the c = 1 Classification

Abstract

Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If $c=1-24k$, there exists a W(2,3k) algebra for k in $Z_{+}/2$ and a W(2,8k) algebra for k in $Z_{+}/4$. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these theories are rational. It is shown, that these non-unitary theories complete the classification of all rational theories with effective central charge $c_{eff}=1$. The results are generalized to the case of extended supersymmetric conformal algebras.

33 pages LaTeX, BONN-HE-92-08

References in corpus (3)

• Structure constants in the N=1 superoperator algebra
• New N=1 Extended Superconformal Algebras with Two and Three Generators
• Representations of $N=1$ Extended Superconformal Algebras with Two Generators

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