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

Abstract

We explore perturbations to a kink-like (codimension 1) topological defect whose world brane is $Ad{S}_q$ embedded into $Ad{S}_{q+1}$. Previously, we found solutions in the limit the mass of the scalar field vanishes. In this article we extend a calculation previously done in $Ad{S}_2$ 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.

23 pages, 6 figures