We construct the nonlinear W(sl(N+3),sl(3)) algebras and find the spectrum of values of the central charge that gives rise, by contracting the W(sl(N+3),sl(3)) algebras, to a W3 algebra belonging to the coset W((sl(N+3),sl(3))/(u(1)⊕sl(N)). Part of the spectrum was conjectured before, but part of it is given here for the first time. Using the tool of embedding the W(sl(N+3),sl(3)) algebras into linearizing algebras, we construct new realizations of W3 modulo null fields. The possibility to predict, within the conformal linearization framework, the central charge spectrum for minimal models of the nonlinear W(sl(N+3),sl(3)) algebras is discussed at the end.
S. et al. (Tue,) studied this question.
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