Kinks in higher derivative scalar field theory

TL;DR

This paper investigates static kink solutions in a two-dimensional higher derivative scalar field theory, analyzing their stability, constructing solutions via a superpotential formalism, and exploring twinlike models.

Contribution

It introduces a superpotential formalism for analytical kink solutions and explores twinlike models in higher derivative scalar theories.

Findings

Linear spectrum described by supersymmetric quantum mechanics

Analytical criteria for stable static solutions

New explicit kink solution constructed

Abstract

We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is analyzed. We find that, the linear spectrum can be described by a supersymmetric quantum mechanics problem, and the criteria for stable static solutions can be given analytically. We also construct a superpotential formalism for finding analytical static kink solutions. Using this formalism we first reproduce some existed solutions and then offer a new solution. The properties of our solution is studied and compared without those preexisted. We also show the possibility in constructing twinlike model in the higher derivative theory, and give the consistency conditions for twinlike models corresponding to the canonical scalar field theory.