Unifying Monopole and Center Vortex as the Semiclassical Confinement Mechanism

Abstract

Magnetic excitations play a crucial role in understanding the color confinement of $4$d Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of $4$d Yang-Mills theory, we can achieve different weakly-coupled descriptions of confinement phenomena: The monopole mechanism takes place on ${\mathbb{R}}^3\times S^1$ with the double-trace deformation, and the center-vortex mechanism is effective on ${\mathbb{R}}^2\times T^2$ with the 't Hooft flux. We unify these two semiclassical descriptions by showing the explicit relation between the monopole and center vortex.

6 pages, 1 figure, v2: clarifications and references added

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Cited by in corpus (6)

• Ensembles of center vortices and chains: Insights from a natural lattice framework
• Monopole-vortex continuity of $\mathcal{N}=1$ super Yang-Mills theory on ${\mathbb{R}}^2\times S^1\times S^1$ with 't Hooft twist
• ${\mathbb{Z}}_N$ stability and continuity in twisted Eguchi-Kawai model with two-flavor adjoint fermions
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• Study of the Emergence of a Gluon Mass Scale from Center Vortices Using a Wave-Functional Formalism
• Thick oriented and nonoriented center-vortex $SU(N)$ configurations with fractional topological charge lumps