  We compute the one-loop world-sheet correction to partition function of
$AdS_5 \times S^5$ superstring that should be representing $k$-fundamental
circular Wilson loop in planar limit. The 2d metric of the minimal surface
ending on $k$-wound circle at the boundary is that of a cone of $AdS_2$ with
deficit $2\pi (1-k)$. We compute determinants of 2d fluctuation operators by
first constructing heat kernels of scalar and spinor Laplacians on the cone
using the Sommerfeld formula. The final expression for the k-dependent part of
the one-loop correction has simple integral representation but is different
from earlier results.
