A $\kappa$-Symmetry Calculus for Superparticles

TL;DR

This paper introduces a new calculus for $ppa$-symmetry in superparticles, enabling the construction of higher order invariant actions by reformulating models as superconformal sigma models.

Contribution

It develops a $ppa$-symmetry calculus for superparticles that avoids using worldline supergravity multiplets, linking $ppa$-symmetry with superconformal symmetry.

Findings

Constructed higher order $ppa$-invariant actions.

Reformulated superparticle models as superconformal sigma models.

Established a $ppa$-calculus equivalent to tensor calculus for superconformal symmetry.

Abstract

We develop a $\kappa$-symmetry calculus for the d=2 and d=3, N=2 massive superparticles, which enables us to construct higher order $\kappa$-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the $\kappa$-symmetry is embedded in the superconformal symmetry so that a calculus for the $\kappa$-symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a worldline supergravity multiplet.