Q-balls, Integrability and Duality

TL;DR

This paper explores the dynamics, interactions, and duality of Q-balls in (1+1)-dimensions, demonstrating how integrability influences their behavior and revealing a duality between Q-balls and kinks.

Contribution

It introduces an integrable model with exact multi-Q-ball solutions and explains the dynamics of Q-balls in non-integrable theories, including a duality with kinks.

Findings

Q-balls can attract or repel depending on their internal phase.

Small Q-balls tend towards integrable dynamics as charge decreases.

A duality exists between stationary Q-balls and static kinks.

Abstract

This paper is concerned with the dynamics and interactions of Q-balls in (1+1)-dimensions. The asymptotic force between well-separated Q-balls is calculated to show that Q-balls can be attractive or repulsive depending upon their relative internal phase. An integrable model with exact multi-Q-ball solutions is investigated and found to be of use in explaining the dynamics in non-integrable theories. In particular, it is demonstrated that the dynamics of small Q-balls in a generic class of non-integrable models tends towards integrable dynamics as the charge decreases. Long-lived oscillations of a single Q-ball can also be understood in terms of a deformation of an exact breather solution in the integrable model. Finally, we show that any theory with Q-ball solutions has a dual description in which a stationary Q-ball is dual to a static kink, with an interchange of Noether and topological charges.