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

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.