English

Geometric analysis of the Yang-Mills-Higgs-Dirac model

Mathematical Physics 2022-09-27 v3 Analysis of PDEs Differential Geometry math.MP

Abstract

The harmonic sections of the Kaluza-Klein model can be seen as a variant of harmonic maps with additional gauge symmetry. Geometrically, they are realized as sections of a fiber bundle associated to a principal bundle with a connection. In this paper, we investigate geometric and analytic aspects of a model that combines the Kaluza-Klein model with the Yang-Mills action and a Dirac action for twisted spinors. In dimension two we show that weak solutions of the Euler-Lagrange system are smooth. For a sequence of approximate solutions on surfaces with uniformly bounded energies we obtain compactness modulo bubbles, namely, energy identities and the no-neck property hold.

Keywords

Cite

@article{arxiv.1908.00430,
  title  = {Geometric analysis of the Yang-Mills-Higgs-Dirac model},
  author = {Jürgen Jost and Enno Keßler and Ruijun Wu and Miaomiao Zhu},
  journal= {arXiv preprint arXiv:1908.00430},
  year   = {2022}
}

Comments

31 pages; accepted manuscript including a slightly extended introduction as well as corrections and clarifications done during review