Abelian Instantons and Monopole Scattering

TL;DR

This paper constructs and analyzes Abelian instantons in QED with monopoles, revealing their role in monopole-catalyzed baryon decay and challenging the assumption that instantons are only non-Abelian.

Contribution

It explicitly constructs Abelian instantons in QED with monopoles and demonstrates their significance in monopole catalysis of baryon decay, expanding the understanding of instanton phenomena.

Findings

Existence of Abelian instantons in QED with monopoles.

Instantons induce 't Hooft zero modes localized around them.

Instantons explain monopole-catalyzed baryon decay with unitarity-saturating cross section.

Abstract

It is usually assumed that $4D$ instantons can only arise in non-Abelian theories. In this paper we re-examine this conventional wisdom by explicitly constructing instantons in an Abelian gauge theory: ${\rm QED}_4$ with $N_f$ flavors of Dirac fermions, in the background of a Dirac monopole. This is the low-energy effective field theory for fermions interacting with a 't Hooft-Polyakov monopole, in the limit where the monopole is infinitely heavy (hence pointlike) and static. This theory, whose non-topological sectors were studied by Rubakov and Callan, has a far richer structure than previously explored. We show how to calculate the topological instanton number, demonstrate the existence of 't Hooft zero modes localized around such instantons, and show how instantons in the path integral provide the underlying mechanism for the Callan-Rubakov process: monopole-catalyzed baryon decay with a cross section that saturates the unitarity bound. Our computation relies on correctly identifying the relevant $2D$ EFT for monopole catalysis as Axial ${\rm QED}_2$ in an effective $AdS_2$ metric.