  Recently a remarkable agreement was found between lattice simulations of long
Wilson lines and behavior of the Nambu Goto string in flat space-time. However,
the latter fails to fit the short distance behavior since it admits a tachyonic
mode for a string shorter than a critical length. In this paper we examine the
question of whether a classical holographic Wilson line can reproduce the
lattice results for Wilson lines of any length. We determine the condition on
the the gravitational background to admit a Coulombic potential at short
distances. We analyze the system using three different renormalization schemes.
We perform an explicit best fit comparison of the lattice results with the
holographic models based on near extremal D3 and D4 branes, non-critical near
extremal AdS6 model and the Klebanov Strassler model. We find that all the
holographic models examined admit after renormalization a constant term in the
potential. We argue that the curves of the lattice simulation also have such a
constant term and we discuss its physical interpretation.
