Microscopic structure of magnetic bions

Abstract

Magnetic bions — stable bound states of monopoles and twisted (“Kaluza-Klein”) anti-monopoles, carrying two units of magnetic charge — have been shown to be the leading cause of confinement and mass gap in four-dimensional gauge theories with massless adjoint fermions compactified on \( {\mathbb{R}^{1,2}} \times {\mathbb{S}^1} \), at least at small \( {\mathbb{S}^1} \). In this paper, we study in detail the bion mechanism and the scales involved for an SU(2) gauge group, using traditional QCD instanton methods. We represent the vacuum functional as the partition function of a bion-anti-bion plasma and obtain the next-to-leading dependence of the mass gap on the \( {\mathbb{S}^1} \) size L at fixed strong-coupling scale Λ. We find that, at small ΛL, the mass gap is an increasing function of L for theories with four massless adjoint Weyl fermions, a case left undetermined by the previous leading-order analysis, and comment on the approach to \( {\mathbb{R}^4} \).