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

2025/05/12 by Hayashi, Yui, Tanizaki, Yuya, Ünsal, Mithat · 2 citations
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2505.07467

Abstract

We consider the semiclassical description of confinement for 4d SU(N) Yang-Mills theory on small ℝ²× T² 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 ℝ³× S¹ 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=8π²/(Ng²). The confinement vacua for NLΛ≪ 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.

Cited by

• Self-dual monopole loops, instantons and confinement
• ℤ_N stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions

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