On the Cohomological Structure of Supersymmetric Lagrangeans With and Without Auxiliary Fields

TL;DR

This paper explores the algebraic cohomological structure underlying supersymmetric Lagrangians, explaining non-renormalization theorems through the perspective of supermultiplet components and supersymmetry variations in key models.

Contribution

It provides a detailed analysis of the cohomological framework of supersymmetric actions, highlighting their representation as highest components of supermultiplets in various models.

Findings

Supersymmetric actions are highest components of supermultiplets.

Supersymmetric interactions can be expressed as supersymmetry variations of lower-dimensional polynomials.

The algebraic structure explains non-renormalization theorems in supersymmetric theories.

Abstract

The origin of non-renormalization theorems in field theories with global supersymmetry can be traced to the fact that supersymmetric actions can be viewed as the highest components of respective supermultiplets. Supersymmetric interactions in particular can therefore be represented as supersymmetry variations of lower dimensional field polynomials. We investigate here this algebraic structure in the context of the Wess-Zumino model and N=1 and N=2 supersymmetric Yang-Mills theories.