Supersymmetric Harmonic Maps into Symmetric Spaces
微分几何
2007-05-23 v1 数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/0511703,
title = {Supersymmetric Harmonic Maps into Symmetric Spaces},
author = {Idrisse Khemar},
journal= {arXiv preprint arXiv:math/0511703},
year = {2007}
}