TL;DR
This paper investigates how adding scalar potentials affects the geometric and analytic properties of Dirac-harmonic maps, highlighting limitations and exploring potentials inspired by supersymmetric quantum field theory.
Contribution
It introduces the impact of scalar potentials on Dirac-harmonic maps and discusses potential benefits and limitations, with a focus on supersymmetry-motivated potentials.
Findings
Potential influences on geometric properties identified
Limitations of potential benefits discussed
Connections to supersymmetric quantum field theory explored
Abstract
We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out that the latter cannot be achieved in general. Finally, we focus on several potentials that are motivated from supersymmetric quantum field theory.
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