A Geometric Formulation of Supersymmetry

TL;DR

This paper introduces a geometric, covariant formulation of supersymmetry that emphasizes the geometric structure of scalar fields as coordinates on a Riemannian manifold, enhancing the understanding of supersymmetric models.

Contribution

It develops a covariant approach to supersymmetry transformations and auxiliary fields, making the geometric nature of supersymmetric theories explicit and applicable to general Riemannian target spaces.

Findings

Covariant supersymmetry transformations for chiral multiplets.

Redefinition of auxiliary fields to ensure covariance.

Manifestly covariant action and transformation laws.

Abstract

The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space.