Perturbations to generalized kink-like topological defects in AdS

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. (C) 2019 The Author(s). Published by Elsevier B.V.