  A calculation of the heavy quark potential at finite temperature at strong
coupling based on the AdS/CFT correspondence is presented. The calculation
relies on the method of complex string trajectories and on the introduction of
a modified renormalization subtraction. The obtained potential is smooth,
negative definite for all quark-antiquark separations, and develops an
imaginary part for r > r_c =0.870/\pi T . At large separations the real part of
the potential does not exhibit the exponential Debye falloff expected from
perturbation theory and instead falls off as a power law, proportional to
1/r^4.
