The "square root" of the Dirac equation and solutions on superspace

TL;DR

This paper derives supersymmetric field equations from the square root of the Dirac operator on superspace, demonstrating solutions for vector and chiral supermultiplets that satisfy massless equations of motion, aiding in constructing renormalizable supersymmetric theories.

Contribution

It introduces a method to derive supersymmetric field equations from the Dirac operator's square root, including solutions for both vector and chiral supermultiplets.

Findings

Vector supermultiplet solution obtained

Chiral supermultiplet solution demonstrated

Both satisfy massless equations of motion

Abstract

The "square root" of the Dirac operator derived on the superspace is used to construct supersymmetric field equations. In addition to the recently found solution - a vector supermultiplet I demonstrate how a chiral supermultiplet follows as the solution. Both vector and chiral supermultiplets are shown to obey appropriate (massless) equations of motion. This procedure yields thus a complete set of fields and their equations necessary to construct renormalizable supersymmetric theories. The problem of masses and interaction is also discussed.