  We consider a non-supersymmetric domain-wall version of $\mathcal{N} = 4$ SYM
theory where five out of the six scalar fields have non-zero classical values
on one side of a wall of codimension one. The classical fields have commutators
which constitute an irreducible representation of the Lie algebra
$\mathfrak{so}(5)$ leading to a highly non-trivial mixing between color and
flavor components of the quantum fields. Making use of fuzzy spherical
harmonics on $S^4$, we explicitly solve the mixing problem and derive not only
the spectrum of excitations at the quantum level but also the propagators of
the original fields needed for perturbative quantum computations. As an
application, we derive the one-loop one-point function of a chiral primary and
find complete agreement with a supergravity prediction of the same quantity in
a double-scaling limit which involves a limit of large instanton number in the
dual D3-D7 probe-brane setup.
