Soliton-fermion systems and stabilised vortex loops

TL;DR

This paper explores the interplay between solitonic solutions and fermionic zero-modes in quantum field theories, highlighting how topological features and fermion coupling influence stability and quantum numbers of these configurations.

Contribution

It analyzes the combined effects of solitons and fermions, particularly zero-energy solutions, on the stability and quantum properties of topological field configurations.

Findings

Fermionic zero-modes can localize on solitons, affecting their quantum numbers.

Topological boundary conditions determine the existence of stable solitonic solutions.

Fermion-soliton interactions can lead to stabilized vortex loops.

Abstract

In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories \cite{Hooft1974} \cite{Polyakov1974} or the skyrme model of hadrons have been proposed as possible non-perturbative bound states which remain stable due to topological quantum numbers. Furthermore when fermions are introduced, under certain conditions one obtains zero-energy solutions \cite{Vega1978}\cite{Jackiw1981} for the Dirac equations localised on the soliton. An implication of such zero-modes is induced fermion number \cite{Jackiw1977} carried by the soliton.