Anomalous Abelian solitons

TL;DR

This paper investigates anomalous Abelian solitons in the chiral Abelian Higgs model, revealing their energy scaling, bounds, non-spherical shapes, and providing numerical constructions and theoretical analysis.

Contribution

It provides a detailed numerical and analytical study of anomalous Abelian solitons, including energy bounds, shape properties, and the validity of the thin wall approximation.

Findings

Energy scales as N_{CS}^{3/4} or N_{CS}^{2/3} depending on the potential.

Existence of a lower bound on soliton energy proportional to N_{CS}^{3/4}.

Anomalous solitons are not spherically symmetric and are constructed numerically.

Abstract

The chiral Abelian Higgs model contains an interesting class of solitons found by Rubakov and Tavkhelidze. These objects carry non-zero fermion number $N_F$ (or Chern-Simons number $N_{CS}$, what is the same because of the chiral anomaly) and are stable for sufficiently large $N_F$. In this paper we study the properties of these anomalous solitons. We find that their energy-versus-fermion-number ratio is given by $E\sim N_{CS}^{3/4}$ or $E\sim N_{CS}^{2/3}$ depending on the structure of the scalar potential. For the former case we demonstrate that there is a lower bound on the soliton energy, which reads $E\geq c N_{CS}^{3/4}$, where $c$ is some parameter expressed through the masses and coupling constants of the theory. We construct the anomalous solitons numerically accounting both for Higgs and gauge dynamics and show that they are not spherically symmetric. The thin wall approximation valid for macroscopic solutions with $N_{CS} \gg 1$ is discussed as well.