Applications of chiral supersymmetry for spin fields in self-dual backgrounds

Due to chiral supersymmetry the (nonzero mode) spectral and symmetry properties of a 4-dimensional, self-dual Dirac-Yang-Mills operator $\text{D}$ can be recovered from those of the corresponding scalar Laplacian $D^2$. It is shown that a similar result holds for higher spins, and that in the 4-vector case the super-symmetric partners are $-D^2{1}_4$ and the fluctuation operator. The reduction to $D^2$ is used to simplify previous analyses of the (nonzero mode) spectrum of $\text{D}$ and of the fluctuations for a BPS-monopole, and to explain the Kepler and su(2/2) (super)symmetries of a system studied recently by D’Hoker and Vinet.