A Fueter operator for 3/2-spinors

Abstract

We show the non-compactness of moduli space of solutions of the monopole equations for $3/2$-spinors on a closed 3-manifold is equivalent to the existence of `3/2-Fueter sections' that are solutions of an overdetermined non-linear elliptic differential equation. These are sections of a fiber bundle whose fiber is a special 4-dimensional submanifold of the hyperk\"ahler manifold of center-framed charged one $SU(2)$-instantons on $\mathbf{R}^4$. This fiber bundle does not inherit a hyperk\"ahler structure.