Compact Q-balls in the complex signum-Gordon model

TL;DR

This paper investigates finite-radius Q-balls in the complex signum-Gordon model across one to three dimensions, providing explicit solutions and analyzing their energy-charge relationship.

Contribution

It introduces and analyzes Q-balls with finite radius in the complex signum-Gordon model, including explicit solutions in certain dimensions.

Findings

Q-balls have strictly finite radius in this model.

Total energy scales as a power of the U(1) charge with exponent (d+2)/(d+3).

Explicit solutions are derived for dimensions d=1 and d=3.

Abstract

We discuss Q-balls in the complex signum-Gordon model in d-dimensional space for d=1,2,3. The Q-balls have strictly finite radius. Their total energy is a power-like function of the conserved U(1) charge with the exponent equal to (d+2)/(d+3). In the cases d=1 and d=3 explicit analytic solutions are presented.