Supersymmetric harmonic maps into symmetric spaces

We study supersymmetric harmonic maps from the point of view of integrable systems. We show that the superharmonic maps from R2|2R2|2 into a symmetric space are solutions of an integrable system and that we have a Weierstrass-type representation in terms of holomorphic potentials (as well as of meromorphic potentials). At the end of the paper we show that superprimitive maps from R2|2R2|2 into a 4-symmetric space give us, by restriction to R2R2, solutions of the second elliptic system associated with the previous 4-symmetric space.