Linearizing W-Algebras

Abstract

We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras $W_3$ and $W_3^{(2)}$ can be embedded as subalgebras into some {\em linear} algebras with finite set of currents. Using these linear algebras we find new field realizations of $W_3^{(2)}$ and $W_3$ which could be a starting point for constructing new versions of $W$-string theories. We also reveal a number of hidden relationships between $W_3$ and $W_3^{(2)}$. We conjecture that similar linear algebras can exist for other $W$-algebras as well.

9 pages, LaTeX

References in corpus (1)

• W-symmetry in Conformal Field Theory

Cited by in corpus (11)

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• Note on W3 Realizations of the Bosonic String
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• New Spinor Field Realizations of the Non-Critical $W_3$ String
• Spinor field realizations of the non-critical $W_{2,4}$ string based on the linear $W_{1,2,4}$ algebra
• Physical States and BRST Operators for Higher-spin $W$ Strings
• W$(2,4)$, Linear and Non-local \W-Algebras in Sp(4) Particle Model
• Explicit field realizations of W algebras