Realisations of $W_3$ Symmetry

Abstract

We perform a systematic investigation of free-scalar realisations of the Za\-mo\-lod\-chi\-kov $W_3$ algebra in which the operator product of two spin-three generators contains a non-zero operator of spin four which has vanishing norm. This generalises earlier work where such an operator was required to be absent. By allowing this spin-four null operator we obtain several realisations of the $W_3$ algebra both in terms of two scalars as well as in terms of an arbitrary number $n$ of free scalars. Our analysis is complete for the case of two-scalar realisations.

14 pages, LATEX, UG-6/92

References in corpus (1)

• Singular Contractions of W-algebras

Cited by in corpus (5)

• Higher-spin strings and W minimal models
• W-Strings 93
• Null Fields Realizations of $W_3$ from $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ Algebras
• The W(sl(N+3),sl(3)) algebras and their contractions to W3
• BRST cohomology of the critical $W_4$ string