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.

Mathematics Subject Classification:

58E20 (Primary), 53C43, 53C27 (Secondary)

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Last update of this page 27.09.2022
The paper was originally written on 6.9.2022