Confinement on 3 x ?1 and double-string collapse

We study confining strings in N = 1 supersymmetric SU(N-c) Yang-Mills theory in the semiclassical regime on (1,2)x ?(1). Static quarks are expected to be confined by double strings composed of two domain walls - which are lines in (2) - rather than by a single flux tube. Each domain wall carries part of the quarks' chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all N-alities, except for those between fundamental quarks. We show that, for N-c >= 5, the two domain walls confining unit N-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the N-ality dependence of the string tensions for 2 <= N-c <= 10. Compared to known scaling laws, we find a weaker, almost flat N-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the ?(1) size by including the effect of virtual W-bosons and show that the qualitative features of double-string confinement persist.

Automated summary

The study examines the confinement mechanism of strings in N = 1 supersymmetric SU(N-c) Yang-Mills theory, finding that static quarks are confined by double strings except for those between fundamental quarks. The behavior of confining strings is quantitatively analyzed with the effect of virtual W-bosons, showing that the qualitative features of double-string confinement persist even as the ?(1) size increases.