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

Abstract

Due to chiral supersymmetry the (nonzero mode) spectral and symmetry properties of a 4-dimensional, self-dual Dirac-Yang-Mills operator 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 supersymmetric 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 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.