Covariant Derivation of Effective Actions for SUSY Topological Defects

TL;DR

This paper extends the effective action method to supersymmetric theories, deriving a covariant, supersymmetric, and kappa-invariant low energy description of topological defects in 2D supersymmetric models, with potential for higher-dimensional theories.

Contribution

It introduces a supersymmetric covariant approach to derive effective actions for topological defects, including super-worldline embeddings and geometrical constraints, advancing the understanding of supersymmetric defect dynamics.

Findings

Derived a supersymmetric, kappa-invariant low energy action

Identified super-worldline embeddings in superspace

Established a framework for higher-dimensional supersymmetric theories

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 $\kappa$--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 $\kappa$--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.