  The contributions of scalars and fermions to the null polygonal bosonic
Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are
considered. We first examine the re-summation of scalars at strong coupling.
Then, we disentangle the form of the fermion contribution and show its strong
coupling expansion. In particular, we derive the leading order with the
appearance of a fermion-anti-fermion bound state first and then effective
multiple bound states thereof. This reproduces the string minimal area result
and also applies to the Nekrasov instanton partition function $\mathcal{Z}$ of
the $\mathcal{N}=2$ theories. Especially, in the latter case the method appears
to be suitable for a systematic expansion.
