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

TL;DR

This paper explores how chiral supersymmetry links the spectral properties of spin fields in self-dual backgrounds to scalar operators, simplifying analysis and revealing underlying symmetries.

Contribution

It extends the application of chiral supersymmetry to higher spins and clarifies the spectral and symmetry properties of spin fields in self-dual backgrounds.

Findings

Spectral properties of higher spin fields relate to scalar Laplacians.

Simplification of spectrum analysis for BPS-monopoles.

Identification of super-symmetries in specific physical systems.

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 super-symmetric partners are $-D^21_4$ 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.