  We consider double-winding, triple-winding and multiple-winding Wilson loops
in the $SU(N)$ Yang-Mills gauge theory. We examine how the area law falloff of
the vacuum expectation value of a multiple-winding Wilson loop depends on the
number of color $N$. In sharp contrast to the difference-of-areas law recently
found for a double-winding $SU(2)$ Wilson loop average, we show irrespective of
the spacetime dimensionality that a double-winding $SU(3)$ Wilson loop follows
a novel area law which is neither difference-of-areas nor sum-of-areas law for
the area law falloff and that the difference-of-areas law is excluded and the
sum-of-areas law is allowed for $SU(N)$ ($N \ge 4$), provided that the string
tension obeys the Casimir scaling for the higher representations. Moreover, we
extend these results to arbitrary multi-winding Wilson loops. Finally, we argue
that the area law follows a novel law, which is neither sum-of-areas nor
difference-of-areas law when $N\ge 3$. In fact, such a behavior is exactly
derived in the $SU(N)$ Yang-Mills theory in the two-dimensional spacetime.

High Energy Physics - Theory