Perturbations of a topological defect as a theory of coupled scalar fields in curved space interacting with an external vector potential

The evolution of small irregularities in a topological defect which propagates on a curved background spacetime is examined. These are described by a system of coupled scalar wave equations on the world sheet of the unperturbed defect which is not only manifestly covariant under world-sheet diffeomorphisms but also under local normal frame rotations. The scalars couple both through the surface torsion of the background world sheet geometry which acts as a vector potential and through an effective mass matrix which is a sum of a quadratic in the extrinsic curvature and a linear term in the spacetime curvature. The coupling simplifies enormously for many physically interesting geometries. This introduces a framework for examining the stability of topological defects generalizing both our earlier work on the perturbations of domain walls and the work of Garriga and Vilenkin on perturbations about a class of spherically symmetric defects in de Sitter space.