Covariant Derivation of Effective Actions for SUSY Topological Defects

Abstract

We make a first step to extend to the supersymmetric arena the effective action method, which is used to covariantly deduce the low energy dynamics of topological defects directly from their parent field theory. By focussing on two-dimensional supersymmetric theories we are able to derive the appropriate change of variables that singles out the low energy degrees of freedom. These correspond to super-worldline embeddings in superspace which are subject to a geometrical constraint. We obtain a supersymmetric and $κ$--invariant low energy expansion, with the standard superparticle action as the leading term, which can be used for the determination of higher-order corrections. Our formulation fits quite naturally with the present geometrical description of $κ$--symmetry in terms of the so-called geometrodynamical constraints. It also provides a basis for the exploration of these issues in higher-dimensional supersymmetric theories.