How complete is the classification of W-symmetries?

Abstract

In 2D conformal quantum field theory, we continue a systematic study of W-algebras with two and three generators and their highest weight representations focussing mainly of rational models. We review the known facts about rational models of W(2,#sigma#)-algebras, in particular those models that are not related to some generically existing algebra. However, our new rational models of W-algebras with two generators all belong to one of the known series. The majority of W-algebras with three generators-including the new ones constructed in this letter- can be explained as subalgebras of Casimir algebras. Nonetheless, for one solution of W(2,4,6) we reveal some features that do not fit into the pattern of Casimir algebras or orbifolds thereof. This shows that even a classification of all Casimir algebras (or Toda field theories) will probably fail to classify all rational conformal field theories. (orig.)SIGLEAvailable from TIB Hannover: RN 5063(93-08) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman