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 worldsheet 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 worldsheet 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 of 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. 1