Double-winding Wilson loops in the SU(N) Yang-Mills theory

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 >= 4), provided that the string tension obeys the Casimir scaling for the higher representations. Moreover, we extend these results to arbitrary multiple-winding Wilson loops. Next, we argue that the area law follows a novel law, which is neither sum-of-areas nor difference-of-areas law when N >= 3. In fact, such a behavior is exactly derived in the SU(N) Yang-Mills theory in the two-dimensional spacetime. Finally, we introduce new Wilson loops whose averages are expected to follow the difference-of-areas law even in the SU(N) Yang-Mills theory for N >= 3.