Center-vortex semiclassics with non-minimal 't Hooft fluxes on $\mathbb{R}^2\times T^2$ and center stabilization at large $N$

TL;DR

This paper constructs and analyzes self-dual center vortices with non-minimal 't Hooft fluxes in 4D SU(N) Yang-Mills theory on small rac{2}{ ext{dimensionality}} imes T^2, exploring their role in confinement and center stabilization at large N.

Contribution

It introduces a novel construction of self-dual center vortices with fractional charges from monopoles, providing semiclassical formulas for confinement and testing twist choices for large N stabilization.

Findings

Vortices have fractional magnetic and topological charges.

Semiclassical formulas for  and string tensions are derived.

The twist choice based on Fibonacci sequence supports center stabilization.

Abstract

We consider the semiclassical description of confinement for $4$d $SU(N)$ Yang-Mills theory on small $\mathbb{R}^2\times T^2$ 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 $3$d Abelianized description of $SU(N)$ gauge fields on $\mathbb{R}^3\times S^1$ 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 $S_{\mathrm{YM}}=8\pi^2/(Ng^2)$. The confinement vacua for $NL\Lambda\ll 1$ can be described by the dilute gas approximation of center vortices, and we give the semiclassical formula for the $\theta$ 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.