Linearizing $W_{2,4}$ and $W{B}_2$ Algebras

Abstract

It has recently been shown that the $W_3$ and $W_3^{(2)}$ algebras can be considered as subalgebras in some linear conformal algebras. In this paper we show that the nonlinear algebras $W_{2,4}$ and $W{B}_2$ as well as Zamolodchikov's spin $5/2$ superalgebra also can be embedded as subalgebras into some linear conformal algebras with a finite set of currents. These linear algebras give rise to new realizations of the nonlinear algebras which could be suitable in the construction of $W$-string theories.

arXiv comment13 pages, LaTeX

References in corpus (5)

• W-symmetry in Conformal Field Theory
• The Relation between Quantum W algebras and Lie algebras
• Extensions of the Virasoro Algebra and Gauged WZW Models
• Critical and non-critical W_{2,4} strings
• Linearizing W-Algebras

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• Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond
• Asymptotically flat structure of hypergravity in three spacetime dimensions
• Hypersymmetry bounds and three-dimensional higher-spin black holes
• Thermodynamic Geometry and Hawking Radiation
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Ghost field realizations of the spinor $W_{2,s}$ strings based on the linear W(1,2,s) algebras
• Null Fields Realizations of $W_3$ from $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ Algebras
• New Spinor Field Realizations of the Non-Critical $W_3$ String
• Effective gravity and OSp(N,4) invariant matter
• The W(sl(N+3),sl(3)) algebras and their contractions to W3
• Spinor field realizations of the non-critical $W_{2,4}$ string based on the linear $W_{1,2,4}$ algebra
• Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields
• Spinor Field Realizations of the half-integer $W_{2,s}$ Strings
• Physical States and BRST Operators for Higher-spin $W$ Strings