Kink interactions in $SU(N)\times Z_2$

TL;DR

This paper explores the interactions between different classes of kinks in the $SU(N) imes Z_2$ model, revealing how their internal orientations and charges influence whether they attract or repel, with detailed calculations for $SU(5)$.

Contribution

It provides a comprehensive analysis of kink interactions in $SU(N) imes Z_2$, including explicit interaction potentials and collision outcomes, highlighting the dependence on internal charges and orientations.

Findings

Interaction depends on the trace of the product of kink charges.

Heavier kinks tend to break into lighter kinks during interactions.

Lightest kink-antikink pairs can exhibit both attraction and repulsion.

Abstract

There are $N-1$ classes of kink solutions in $SU(N)\times Z_2$. We show how interactions between various kinks depend on the classes of individual kinks as well as on their orientations with respect to each other in the internal space. In particular, we find that the attractive or repulsive nature of the interaction depends on the trace of the product of charges of the two kinks. We calculate the interaction potential for all combinations of kinks and antikinks in $SU(5)\times Z_2$ and study their collisions. The outcome of kink-antikink collisions, as expected from previous studies, is sensitive to their initial relative velocity. We find that heavier kinks tend to break up into lighter ones, while interactions between the lightest kinks and antikinks in this model can be repulsive as well as attractive.