A Locally Supersymmetric Action for the Scalar Particle

TL;DR

This paper develops a locally supersymmetric action for the scalar particle, linking it to the standard reparametrization invariant form, and offers insights into supersymmetric string formulations without fixing gauges.

Contribution

It introduces a new locally supersymmetric action for the scalar particle and demonstrates its equivalence to the traditional reparametrization invariant action without gauge fixing.

Findings

Established a supersymmetric particle action with local invariance.

Proved equivalence to the standard reparametrization invariant action.

Provided a simplified approach to supersymmetric string formulations.

Abstract

We construct a locally supersymmetric action for the scalar particle, and study its relation with the usual reparametrization invariant action. The mechanisms at work are similar to those employed in the embedding of the bosonic string into the fermionic one, originally due to Berkovits and Vafa in their search for a universal string. The simpler algebraic structure present in the particle case provides us with a guide on how to prove in a simple way, without the need of fixing the superconformal gauge, that the supersymmetric formulation of the bosonic string is equivalent to the usual one, where reparametrization invariance is the only world-sheet gauge symmetry.