Microscopic Structure of Magnetic Bions

TL;DR

This paper investigates the microscopic structure of magnetic bions in SU(2) gauge theories, revealing how they induce confinement and mass gap, with detailed analysis of the dependence on compactification scale using instanton methods.

Contribution

It provides a detailed study of magnetic bions in SU(2) gauge theories, including the scale dependence of the mass gap and the representation of the vacuum as a bion-anti-bion plasma.

Findings

Mass gap increases with S^1 size L at small Lambda L for theories with four massless adjoint fermions.

Representation of the vacuum as a bion-anti-bion plasma.

Next-to-leading order dependence of the mass gap on L is obtained.

Abstract

Magnetic bions---stable bound states of monopoles and twisted ("Kaluza-Klein") 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 R**{1,2} x S**1, at least at small 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 S**1 size L at fixed strong-coupling scale Lambda. We find that, at small Lambda x L, 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 R**4.