Supersymmetric harmonic maps into symmetric spaces

Abstract

We study supersymmetric harmonic maps from the point of view of integrable systems. We show that the superharmonic maps from R 2 | 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 R 2 | 2 into a 4-symmetric space give us, by restriction to R 2 , solutions of the second elliptic system associated with the previous 4-symmetric space.