Perturbations to Kink-Like Topological Defects in 2D Anti de Sitter Spacetime

TL;DR

This paper investigates the stability and perturbations of kink-like topological defects in two-dimensional Anti de Sitter spacetime, extending previous analytical solutions and analyzing their linear stability.

Contribution

It extends prior work by analyzing linear perturbations and stability of topological defects in AdS2, including general features of perturbation expansions.

Findings

Linear perturbations are stable.

Exact solutions are extended to include perturbations.

General features of all-order perturbation expansion are discussed.

Abstract

We examine codimension--1 topological defects whose associated worldline is geodesically embedded in $\AdS_{2}$. This discussion extends a previous study of exact analytical solutions to the equations of motion of topological defects in $\AdS_{n}$ in a particular limit where the masses of the scalar and gauge field vanish. We study the linear perturbations about the zeroth order kink-like solution and verify that they are stable. We also discuss general features of the perturbation expansion to all orders.