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Dirac-harmonic maps with potential.

Volker Branding1

  • 1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

Letters in Mathematical Physics
|July 7, 2022
PubMed
Summary
This summary is machine-generated.

We investigated how adding a scalar potential affects Dirac-harmonic maps. This research explores potential benefits and limitations, with a focus on theories from supersymmetric quantum field theory.

Keywords:
Dirac-harmonic map with potentialRegularitySecond variation

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Area of Science:

  • Mathematical Physics
  • Differential Geometry

Background:

  • Dirac-harmonic maps are crucial in geometric analysis.
  • Scalar potentials can alter the behavior of physical systems.

Purpose of the Study:

  • To analyze the impact of an additional scalar potential on Dirac-harmonic maps.
  • To identify potential benefits and limitations of incorporating such potentials.
  • To explore potentials motivated by supersymmetric quantum field theory.

Main Methods:

  • Geometric analysis of Dirac-harmonic maps.
  • Mathematical formulation of scalar potential effects.
  • Investigation of properties under potential induction.

Main Results:

  • The addition of a scalar potential influences geometric and analytic properties.
  • Not all desired benefits from the potential term are generally achievable.
  • Specific potentials derived from supersymmetric quantum field theory were examined.

Conclusions:

  • Scalar potentials offer a means to modify Dirac-harmonic map properties.
  • The general applicability of potential-induced benefits is limited.
  • Connections between Dirac-harmonic maps and supersymmetric theories are highlighted.