Some Comments on BPS systems

TL;DR

This paper investigates multi-field BPS systems, especially two interacting Sine-Gordon-like fields, analyzing their static solutions, interactions, and dynamics, revealing phase shifts in weak interactions and repulsion in strong ones.

Contribution

It provides a detailed analysis of BPS systems with multiple fields, focusing on two interacting Sine-Gordon-like models and their solitonic interactions.

Findings

Weak interactions allow solitons to pass through with phase shifts.

Strong interactions cause solitons to repel and reflect.

Modified gradient flow visualizes solutions in field space.

Abstract

We look at simple BPS systems involving more than one field. We discuss the conditions that have to be imposed on various terms in Lagrangians involving many fields to produce BPS systems and then look in more detail at the simplest of such cases. We analyse in detail BPS systems involving 2 interacting Sine-Gordon like fields, both when one of them has a kink solution and the second one either a kink or an antikink solution. We take their solitonic static solutions and use them as initial conditions for their evolution in Lorentz covariant versions of such models. We send these structures towards themselves and find that when they interact weakly they can pass through each other with a phase shift which is related to the strength of their interaction. When they interact strongly they repel and reflect on each other. We use the method of a modified gradient flow in order to visualize the solutions in the space of fields.