  As a perturbative check of the construction of four-dimensional (4D) ${\cal
N}=4$ supersymmetric Yang-Mills theory (SYM) from mass deformed ${\cal
N}=(8,8)$ SYM on the two-dimensional (2D) lattice, the one-loop effective
action for scalar kinetic terms is computed in ${\cal N}=4$ $U(k)$ SYM on
${\mathbb R}^2 \times$ (fuzzy $S^2$), which is obtained by expanding 2D ${\cal
N}=(8,8)$ $U(N)$ SYM with mass deformation around its fuzzy sphere classical
solution. The radius of the fuzzy sphere is proportional to the inverse of the
mass. We consider two successive limits: (1) decompactify the fuzzy sphere to a
noncommutative (Moyal) plane and (2) turn off the noncommutativity of the Moyal
plane. It is straightforward at the classical level to obtain the ordinary
${\cal N}=4$ SYM on ${\mathbb R}^4$ in the limits, while it is nontrivial at
the quantum level. The one-loop effective action for $SU(k)$ sector of the
gauge group $U(k)$ coincides with that of the ordinary 4D ${\cal N}=4$ SYM in
the above limits. Although "noncommutative anomaly" appears in the overall
$U(1)$ sector of the $U(k)$ gauge group, this can be expected to be a gauge
artifact not affecting gauge invariant observables.
