  Applying the AdS/CFT correspondence, the expansion of the heavy-quark
potential of the ${\cal N}=4$ supersymmetric Yang-Mills theory at large $N_c$
is carried out to the sub-leading term in the large 't Hooft coupling at zero
temperature. The strong coupling corresponds to the semi-classical expansion of
the string-sigma model, the gravity dual of the Wilson loop operator, with the
sub-leading term expressed in terms of functional determinants of fluctuations.
The singularities of these determinants are examined and their contributions
are evaluated numerically.
