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

## TL;DR

This paper explores the geometric and analytic properties of a combined Kaluza-Klein, Yang-Mills, and Dirac model, demonstrating regularity and compactness results for solutions on surfaces with bounded energy.

## Contribution

It introduces a geometric framework for the Yang-Mills-Higgs-Dirac model and proves regularity and compactness results for solutions in two dimensions.

## Key findings

- Weak solutions are smooth in dimension two.
- Energy identities hold for sequences of approximate solutions.
- No-neck property ensures compactness modulo bubbles.

## 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.