Linearization of thick K-branes

TL;DR

This paper investigates the linear stability and spectral properties of thick K-branes generated by scalar fields with nonstandard kinetic terms, revealing conditions for stability and the nonlocalizability of scalar perturbations.

Contribution

It provides a detailed analysis of linear perturbations of thick K-branes, deriving master equations and stability conditions using supersymmetric quantum mechanics.

Findings

Scalar perturbations are generally nonlocalizable.

Conditions for stable K-branes are identified.

Spectra of normal modes are characterized.

Abstract

We study the linearization of a class of thick K-branes, namely, four-dimensional domain walls generated by a scalar field with particular nonstandard kinetic terms. The master equations for linear perturbations are derived from the point of view of both dynamical equations and quadratic action. The spectra of the canonical normal modes are studied using supersymmetric quantum mechanics. Our results indicate that the scalar perturbation is nonlocalizable in general. Conditions for stable $K$-branes are also found.