Abstract: I will start by describing the Dirac-Yang-Mills system on a Riemannian manifold. This is a coupled system of elliptic PDEs involving connections on and sections of vector bundles over the base manifold. It has its origins in physics where, posed on a spacetime, it describes the interaction between fermions (such as electrons) and a force field.
The Dirac-Yang-Mills system are the Euler-Lagrange equations of the Dirac-Yang-Mills action functional. However, this is unbounded in both directions, making proving existence of critical points challenging. In this talk I will therefore present a result which in many cases allows for the Dirac-Yang-Mills system
to be decoupled into a pair of equations (the Yang-Mills and the Dirac equation) which are significantly easier to treat and which have been more extensively
studied in the Riemannian setting. I will describe how an application of analytic perturbation theory gives an elegant characterization of precisely when this can
be done.