  Following Polchinski and Sully (arXiv:1104.5077), we consider a generalized
Wilson loop operator containing a constant parameter $\zeta$ in front of the
scalar coupling term, so that $\zeta=0$ corresponds to the standard Wilson
loop, while $\zeta=1$ to the locally supersymmetric one. We compute the
expectation value of this operator for circular loop as a function of $\zeta$
to second order in the planar weak coupling expansion in N=4 SYM theory. We
then explain the relation of the expansion near the two conformal points
$\zeta=0$ and $\zeta=1$ to the correlators of scalar operators inserted on the
loop. We also discuss the $AdS_5\times S^5$ string 1-loop correction to the
strong-coupling expansion of the standard circular Wilson loop, as well as its
generalization to the case of mixed boundary conditions on the five-sphere
coordinates, corresponding to general $\zeta$. From the point of view of the
defect 1d CFT defined on the Wilson line, the $\zeta$-dependent term can be
seen as a perturbation driving a RG flow from the standard Wilson loop in the
UV to the supersymmetric Wilson loop in the IR. Both at weak and strong
coupling we find that the logarithm of the expectation value of the standard
Wilson loop for the circular contour is larger than that of the supersymmetric
one, which appears to be in agreement with the 1d analog of the F-theorem.
