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arXiv · hep-th/9609038

The W(sl(N+3),sl(3)) algebras and their contractions to W3

S. Bellucci·S. Krivonos·A. Sorin
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Abstract

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 $W_3$ algebra belonging to the coset $W((sl(N+3),sl(3))/(u(1)\oplus sl(N))$. 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 $W_3$ 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.

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S. Bellucci, S. Krivonos, A. Sorin. 1996-09-04. The W(sl(N+3),sl(3)) algebras and their contractions to W3. https://doi.org/10.1016/s0370-2693(96)01562-6

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