  We give evidence that spacelike BPS Wilson loops do not exist in Minkowski
spacetime. We show that spacelike Wilson loops in Minkowski spacetime cannot
preserve any supersymmetries, in $d = 4$ $\mathcal N = 4$ super Yang-Mills
theory, $d = 3$ $\mathcal N = 2$ super Chern-Simons-matter theory, and $d = 3$
$\mathcal N = 6$ Aharony-Bergman-Jafferis-Maldacena theory. We not only show
this using infinite straight lines and circles as examples, but also we give
proofs for general curves. We attribute this to the conflicts of reality
conditions of the spinors. However, spacelike Wilson loops do exist in
Euclidean space. There are both BPS Wilson loops along infinite straight lines
and circular BPS Wilson loops. This is because the reality conditions of the
spinors are lost after Wick rotation. The result is reasonable in view of the
AdS/CFT correspondence.
