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Pré-Publication, Document De Travail Année : 2005

Supersymmetric Harmonic Maps into Symmetric Spaces.

Idrisse Khemar
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Résumé

We study supersymmetric harmonic maps from the point of view of integrable system. It is well known that harmonic maps from R^2 into a symmetric space are solutions of a integrable system . We show here that the superharmonic maps from R^{2|2} into a symmetric space are solutions of a integrable system, more precisely of a first elliptic integrable system in the sense of C.L. Terng and that we have a Weierstrass-type representation in terms of holomorphic potentials (as well as of meromorphic potentials). In the end of the paper we show that superprimitive maps from R^{2|2} into a 4-symmetric space give us, by restriction to R^2, solutions of the second elliptic system associated to the previous 4-symmetric space.
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Dates et versions

hal-00014688 , version 1 (29-11-2005)

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Idrisse Khemar. Supersymmetric Harmonic Maps into Symmetric Spaces.. 2005. ⟨hal-00014688⟩
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