Kinks bounded by fermions

Ilya Perapechka,Yakov Shnir

doi:10.1103/physrevd.101.021701

Abstract

We present and study new mechanism of interaction between the solitons based on the exchange interaction mediated by the localized fermion states. As particular examples, we consider solutions of simple 1+1 dimensional scalar field theories with self-interaction potentials, including sine-Gordon model and the polynomial $\phi^4$, $\phi^6$ models, coupled to the Dirac fermions with back-reaction. We discover that there is an additional fermion exchange interaction between the solitons, it leads to the formation of static multi-soliton bound states. Further, we argue that similar mechanisms of formation of stable coupled multi-soliton configurations can be observed for a wide class of physical systems.

Highlights

IntroductionOne of the most interesting features of the topological solitons, like kinks, vortices, or monopoles (see, e.g., [1,2]), is the remarkable relation between the topological charge of the configuration and the number of fermionic zero modes localized on a soliton
One of the most interesting features of the topological solitons, like kinks, vortices, or monopoles, is the remarkable relation between the topological charge of the configuration and the number of fermionic zero modes localized on a soliton
We found that the backreaction of the localized fermions significantly modifies both the spectral flow and the structure of the coupled configurations

Summary

Introduction

One of the most interesting features of the topological solitons, like kinks, vortices, or monopoles (see, e.g., [1,2]), is the remarkable relation between the topological charge of the configuration and the number of fermionic zero modes localized on a soliton. The fermion zero modes of solitons have been studied for many decades; these states localized on the vortices were discussed first in Ref. There has been substantial interest in the study of these localized states in various dimensions; examples are fermion modes of the kinks [5,6,7,8], monopoles [9,10], sphalerons [11,12], and skyrmions [13,14,15,16]. The existence of localized fermions leads to many interesting and unusual phenomena such as fermion number fractionization [6,17], monopole catalysis [9,10], and string superconductivity in cosmology [18] or in chiral superconductors [19]

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Conclusion