Massless monopole-string-domain wall fermions and polyhedral vacuum fermions

TL;DR

This paper analytically investigates fermion zero modes in monopole-string-domain wall systems, revealing their localization, confinement in polyhedral shapes, and conditions for superconducting currents, advancing understanding of soliton-fermion interactions.

Contribution

It provides an analytical solution for fermion zero modes in complex soliton composites and introduces the concept of polyhedral vacuum fermions with specific confinement properties.

Findings

Existence of one fermion zero mode in monopole-string-domain wall systems.

Zero modes are localized on monopoles, strings, or walls depending on parameters.

Fermionic superconducting currents are limited to specific soliton configurations.

Abstract

Fermion zero modes of Bogomol'nyi-Prasad-Sommerfield monopole-string-domain wall composites in three spatial dimensions are studied. We analytically solve the Dirac equation and prove the existence of one fermion zero mode. Depending on mass parameters of bosons/fermions in the model, the zero modes are localized either on the monopoles, strings or domain walls, which we call monopole-string-domain wall fermions. We also show that in special cases, the zero modes can be confined within a finite vacuum region in the shape of an arbitrary convex polyhedron, which we call the polyhedral vacuum fermions. Furthermore, we show that fermionic superconducting currents do not generally flow on the host solitons except for the cases that the soliton network consists only of strings and domain walls and has translational symmetry about a spatial axis.