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

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

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  • 发表日期：

    2026年2月11日

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  • Yui Hayashi,
  • Yuya Tanizaki,
  • Mithat Ünsal

摘要

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 SYM = 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 = Fn+2 and p = Fn, suggested in studies of the twisted Eguchi-Kawai model, from the viewpoint of the 1-form and 0-form center symmetries.