Weil Algebras and Supersymmetry

TL;DR

This paper offers a novel interpretation of super loop space in supersymmetry using Weil algebras, connecting fermionic coordinates with algebra generators and exploring implications for various supersymmetric theories.

Contribution

It introduces a new perspective on super loop space through Weil algebras, unifying supersymmetric multiplets and auxiliary fields in a geometric framework.

Findings

Weil algebra interpretation of fermionic coordinates in super loop space.

Application to N=1 supermultiplet, supersymmetric quantum mechanics, Wess-Zumino, and Yang-Mills theories.

Insights into constrained systems, integrable models, and non-Abelian localization.

Abstract

We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are the auxiliary fields. The general N=1 supermultiplet is interpreted in terms of Weil algebras. As specific examples we consider supersymmetric quantum mechanics, Wess-Zumino model and supersymmetric Yang-Mills theory in four dimensions. Some comments on the formulation of constrained systems and integrable models and non-Abelian localization are given.