Toward the construction of N=2 supersymmetric integrable hierarchies

Details Toward the construction of N=2 supersymmetric integrable hierarchies Toward the construction of N=2 supersymmetric integrable hierarchies

1996-04-25

arxiv.org/abs/hep-th/9604165v3

Nucl.Phys. B477 (1996) 835-854

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, Latex, a few more misprints have been corrected

Scientific paper

10.1016/0550-3213(96)00377-X

We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible $N=2$ supersymmetric integrable hierarchies with $N=2$ super $W_n$ second hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the $N=2$ supersymmetric extensions of the Generalized Non-Linear Schr\"{o}dinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct hamiltonians we are led to a new definition of super-residues for degenerate N=2 supersymmetric pseudodifferential operators. We have found a new non-polinomial Miura-like realization for $N=2$ superconformal algebra in terms of two bosonic chiral--anti--chiral free superfields.

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