# Perturbations to Generalized Kink-like Topological Defects in $AdS$

## TL;DR

This paper investigates the stability of perturbations to kink-like topological defects in anti-de Sitter spaces, extending previous work to higher dimensions and demonstrating stability of scalar field perturbations.

## Contribution

It generalizes earlier results by analyzing perturbations in higher-dimensional $AdS$ embeddings and shows their stability at first order.

## Key findings

- All perturbations to the scalar field mass are stable to first order.
- The equation of motion for perturbations resembles a well-known quantum mechanics problem.
- Extended analysis from $AdS_2$ to higher-dimensional $AdS$ spaces.

## Abstract

We explore perturbations to a kink-like (codimension 1) topological defect whose world brane is $AdS_{q}$ embedded into $AdS_{q+1}$. Previously, we found solutions in the limit the mass of the scalar field vanishes. In this article we extend a calculation previously done in $AdS_{2}$ to higher-dimensional embedding spaces and find that all perturbations to the mass of the field are stable to first order as expected in a theory with topological defects. We find that the equation of motion to the correction strongly resembles a problem well-known in quantum mechanics.