Nontopological Electromagnetic Hedgehogs

TL;DR

This paper investigates classical localized solitons in a complex Proca field theory with global U(1) symmetry, focusing on nonrelativistic, spherically symmetric solutions that can source electromagnetic fields through specific couplings.

Contribution

It introduces the concept of nontopological electromagnetic hedgehogs supported by quartic interactions in a complex Proca field and analyzes their existence conditions and properties.

Findings

Existence conditions for electromagnetic hedgehogs are established.

Spherical symmetric solitons can source electric or magnetic fields.

The properties of these solitons depend on parity-even or parity-odd couplings.

Abstract

We study classical localised configurations - solitons - in a theory of self-interacting complex Proca field with the global $U(1)$ symmetry. We focus on spherically-symmetric solitons near the nonrelativistic limit, which are supported by the quartic interactions of the neutral Proca field. Such solitons can source the radial electric (magnetic) field if one introduces a parity-even (parity-odd) coupling of the Proca field to the electromagnetic field tensor. We discuss the conditions of existence of such nontopological ''electromagnetic hedgehogs'' and their properties.