W-Algebras of Negative Rank

Abstract

Recently it has been discovered that the W-algebras (orbifold of) WD_n can be defined even for negative integers n by an analytic continuation of their coupling constants. In this letter we shall argue that also the algebras WA_{-n-1} can be defined and are finitely generated. In addition, we show that a surprising connection exists between already known W-algebras, for example between the CP(k)-models and the U(1)-cosets of the generalized Polyakov-Bershadsky-algebras.

12 papes, Latex, preprint DFTT-40/94

References in corpus (8)

• W-symmetry in Conformal Field Theory
• Beyond the Large N Limit: Non-linear W(infinity) as symmetry of the SL(2,R)/U(1) coset model
• Poisson-Lie group of pseudodifferential symbols
• Unifying W-Algebras
• W-algebras with set of primary fields of dimensions (3, 4, 5) and (3,4,5,6)
• How Complete is the Classification of W-Symmetries ?
• A Class of W-Algebras with Infinitely Generated Classical Limit
• Classification of Structure Constants for W-algebras from Highest Weights

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