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Conformal Linearization Versus Nonlinearity of $W$-Algebras

S. Krivonos·A. Sorin
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Abstract

We review the new approach to the theory of nonlinear $W$-algebras which is developed recently and called {\it conformal linearization}. In this approach $W$-algebras are embedded as subalgebras into some {\it linear conformal} algebras with a finite set of currents and most of their properties could be understood in a much simpler way by studing their linear counterpart. The general construction is illustrated by the examples of $u(N)$-superconformal, $W(sl(N),sl(2))$, $W(sl(N),sl(N))$ as well as $W(sl(N),sl(3))$ algebras. Applications to the construction of realizations (included modulo null fields realizations) as well as central charge spectrum for minimal models of nonlinear algebras are discussed. (To appear in ``Geometry and Integrable Models'', Eds.: P.N.Pyatov & S.N.Solodukhin, World Scientific Publ. Co. (in press)).

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S. Krivonos, A. Sorin. 1995-10-15. Conformal Linearization Versus Nonlinearity of $W$-Algebras. https://arxiv.org/abs/hep-th/9510072

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