Supersymmetric Harmonic Maps into Symmetric Spaces

2005/11/29 by Idrisse Khemar, Khemar, Idrisse
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.math/0511703

arxiv created 2005/11/29 · openalex publication_date 2005/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study supersymmetric harmonic maps from the point of view of integrable system. It is well known that harmonic maps from R² 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 R², solutions of the second elliptic system associated to the previous 4-symmetric space.

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