The $N=2$ super $W_4$ algebra and its associated generalized KdV hierarchies

Details The $N=2$ super $W_4$ algebra and its associated generalized KdV hierarchies The $N=2$ super $W_4$ algebra and its associated generalized KdV hierarchies

1993-01-19

arxiv.org/abs/hep-th/9301077v1

J.Math.Phys. 34 (1993) 4050-4063

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, LaTeX, UTAS-PHYS-92-32

Scientific paper

10.1063/1.530025

We construct the $N=2$ super $W_4$ algebra as a certain reduction of the second Gel'fand-Dikii bracket on the dual of the Lie superalgebra of $N=1$ super pseudo-differential operators. The algebra is put in manifestly $N=2$ supersymmetric form in terms of three $N=2$ superfields $\Phi_i(X)$, with $\Phi_1$ being the $N=2$ energy momentum tensor and $\Phi_2$ and $\Phi_3$ being conformal spin $2$ and $3$ superfields respectively. A search for integrable hierarchies of the generalized KdV variety with this algebra as Hamiltonian structure gives three solutions, exactly the same number as for the $W_2$ (super KdV) and $W_3$ (super Boussinesq) cases.

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