Susy Hierarchies and Affine Algebras

Details Susy Hierarchies and Affine Algebras Susy Hierarchies and Affine Algebras

1997-10-04

arxiv.org/abs/solv-int/9710001v1

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTex, uses lamuphys.sty: talk given at the UIC ``Supersymmetry and Integrable Systems Workshop'', Chicago, June 12-

Scientific paper

10.1007/BFb0105325

We review some basic features of the Lie-algebraic classification of W-algebras and related integrable hierarchies in 1+1 dimensions, pointing out the role of affine Lie algebras. We emphasize that the supersymmetric extensions of the above construction possibly lead, though some questions are still opened, to the classification of supersymmetric hierarchies based on ``generic'' supersymmetric affine Lie algebras. Here the word generic is used to make clear that well-known procedures, as those introduced by Inami and Kanno, are too restricted and do not lead to the full spectrum of supersymmetric integrable hierarchies one can construct. A particular attention is devoted to the large-N supersymmetric extensions (here N=4). The attention paid by large-N theories being due to the fact that they arise as dimensional reduction of N=1 models, and moreover that they realize an ``unification'' of known hierarchies.

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