The Dirac–Higgs bundle is a vector bundle with a natural connection on the moduli space of stable Higgs bundles on a compact Riemann surface. It is a vector bundle of null-spaces of a Dirac-operator coupled to stable Higgs bundles. In this thesis, we study various aspects of this bundle and its natural connection.

The Dirac–Higgs bundle is hyperholomorphic on the smooth hyperkähler moduli space of stable Higgs bundles. This property is a generalisation of the four-dimensional anti- ...