Kink-boundary collisions in a two dimensional scalar field theory

TL;DR

This study investigates kink-boundary collisions in a 2D scalar field model inspired by heterotic M-theory, revealing inelastic reflections, radiation emission, and a tendency toward a final state with multiple kinks.

Contribution

It provides the first numerical and analytical analysis of kink-boundary collisions in this model, showing inelastic reflection and the spontaneous generation of multiple kinks.

Findings

Kinks are always inelastically reflected with energy loss to radiation.

Radiation emission leads to a bulk populated with many kinks.

The final state likely consists of a stack of kinks determined by initial energy.

Abstract

In a two-dimensional toy model, motivated from five-dimensional heterotic M-theory, we study the collision of scalar field kinks with boundaries. By numerical simulation of the full two-dimensional theory, we find that the kink is always inelastically reflected with a model-independent fraction of its kinetic energy converted into radiation. We show that the reflection can be analytically understood as a fluctuation around the scalar field vacuum. This picture suggests the possibility of spontaneous emission of kinks from the boundary due to small perturbations in the bulk. We verify this picture numerically by showing that the radiation emitted from the collision of an initial single kink eventually leads to a bulk populated by many kinks. Consequently, processes changing the boundary charges are practically unavoidable in this system. We speculate that the system has a universal final state consisting of a stack of kinks, their number being determined by the initial energy.