# Are all Dirac-harmonic maps uncoupled?

by

Bernd Ammann

**Are all Dirac-harmonic maps uncoupled?**

Former Title: *On triviality of Dirac-harmonic maps*

Preprint version (pdf)

Arxiv link: math>arXiv:2209.03074, (pdf)

### Abstract

Dirac-harmonic maps (f,φ) consist of a map f:M→ N and a twisted spinor φ∈Γ(Σ M⊗ f^{*}TN) and they are defined as critical points of the super-symmetric energy functional.

A Dirac-harmonic map is called uncoupled, if f is a harmonic map.

We show that under some minimality assumption Dirac-harmonic maps defined on a closed domain are uncoupled.

This raises the question whether all Dirac-harmonic maps with closed domain are uncoupled.

58E20 (Primary), 53C43, 53C27 (Secondary)
### Additional information

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Last update of this page 27.09.2022

The paper was originally written on 6.9.2022