Instantons in the Maximally Abelian Gauge

We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$ instanton in continuum gauge theory. We find that there is a class of solutions to the differential MA gauge condition with circular monopole loops of radius $R$ centered on the instanton of width $\rho$. However, the MA gauge fixing functional $G$ decreases monotonically as $R\mathrm{/}\rho \to 0$. Its global minimum is the instanton in the singular gauge. We point out that interactions with nearby anti-instantons are likely to excite these monopole loops.