Center-vortex semiclassics with non-minimal ’t Hooft fluxes on ℝ2 × T2 and center stabilization at large N

A bstract We consider the semiclassical description of confinement for 4d SU( N ) Yang-Mills theory on small ℝ 2 × T 2 with non-minimal ’t Hooft twist p with gcd( N , p ) = 1. For this purpose, we construct the self-dual center vortex for non-minimal ’t Hooft twists from the Kraan-van Baal-Lee-Lu-Yi (KvBLLY) monopoles by using the 3d Abelianized description of SU( N ) gauge fields on ℝ 3 × S 1 with nontrivial holonomy backgrounds. This construction shows the self-dual vortex has (1) the fractional magnetic charge q / N with pq = 1 mod N , (2) the fractional topological charge 1/ N , and (3) the fractional instanton action S YM = 8 π 2 /( Ng 2 ). The confinement vacua for NL Λ ≪ 1 can be described by the dilute gas approximation of center vortices, and we give the semiclassical formula for the θ dependence and confining string tensions. We apply this result to understand the suitable choice of the twist p for center stabilization at large N . In particular, we test the proposal using the Fibonacci sequence, N = F n +2 and p = F n , suggested in studies of the twisted Eguchi-Kawai model, from the viewpoint of the 1-form and 0-form center symmetries.