  We analyze the structure of the UV divergences of the Wilson loop for a
general gauge/gravity duality. We find that, due to the presence of a
nontrivial NSNS B-field and metric, new divergences that cannot be subtracted
out by the conventional Legendre transform may arise. We also derive conditions
on the B-field and the metric, which when satisfied, the leading UV divergence
will become linear, and can be cancelled out by choosing the boundary condition
of the string appropriately. Our results, together with the recent result of
arXiv:0807.5127, where the effect of a nontrivial dilaton on the structure of
UV divergences in Wilson loop is analysed, allow us to conclude that Legendre
transform is at best capable of cancelling the linear UV divergences arising
from the area of the worldsheet, but is incapable to handle the divergences
associated with the dilaton or the B-field in general. We also solve the
conditions for the cancellation of the leading linear divergences generally and
find that many well-known supergravity backgrounds are of these kinds,
including examples such as the Sakai-Sugimoto QCD model or N=1 duality with
Sasaki-Einstein spaces. We also point out that Wilson loop in the
Klebanov-Strassler background have a divergence associated with the B-field
which cannot be cancelled away with the Legendre transform. Finally we end with
some comments on the form of the Wilson loop operator in the ABJM
superconformal Chern-Simons theory.
