Supersymmetric Skyrmions : Numerical Solutions

TL;DR

This paper numerically finds supersymmetric skyrmion solutions in the ${ m N}=1$ Skyrme model, overcoming challenges of higher derivative equations by using perturbation methods to demonstrate existence up to second order.

Contribution

It introduces a numerical approach to supersymmetric skyrmions in a higher derivative model and applies perturbation techniques to find solutions.

Findings

Supersymmetric skyrmion solutions exist up to second order in coupling.

Direct solutions lead to runaway behavior, necessitating perturbation methods.

The approach confirms the existence of solutions in a complex higher derivative context.

Abstract

We consider the ${\cal N}=1$ Skyrme model and obtain supersymmetric skyrmion solutions numerically. The model necessarily contains higher derivative terms and as a result the field equation becomes a fourth-order differential equation. Solving the equation directly leads to runaway solutions as expected in higher derivative theories. We, therefore, apply the perturbation method and show that skyrmion solutions exist upto the second order in the coupling constant.