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 pr opagates on a curved background spacetime is examined. These are descr ibed by a system of coupled scalar wave equations on the world sheet o f the unperturbed defect which is not only manifestly covariant under world-sheet diffeomorphisms but also under local normal frame rotation s. The scalars couple both through the surface torsion of the backgrou nd world sheet geometry which acts as a vector potential and through a n 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 def ects generalizing both our earlier work on the perturbations of domain walls and the work of Garriga and Vilenkin on perturbations about a c lass of spherically symmetric defects in de Sitter space.