Confinement on ℝ3 × 𝕊1 and double-string collapse

Abstract

Abstract We study confining strings in $$ \mathcal{N} $$ N = 1 supersymmetric SU(Nc) Yang-Mills theory in the semiclassical regime on ℝ1,2× 𝕊1. Static quarks are expected to be confined by double strings composed of two domain walls — which are lines in ℝ2 — 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 Nc≥ 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 ≤ Nc≤ 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 𝕊1 size by including the effect of virtual “W-bosons” and show that the qualitative features of double-string confinement persist.