'Just another field theory' approach to $\mathcal{N}$=1 Super Yang-Mills and the origin of intrinsic SuperGeometry

TL;DR

This paper introduces a novel, non-geometric derivation of $ abla$=1 Super Yang-Mills theory using a superspace approach, revealing its geometric structure without assuming gauge invariance, and simplifies the interaction description.

Contribution

It provides a new derivation method for $ abla$=1 Super Yang-Mills that avoids gauge assumptions and presents the theory as a finite polynomial, clarifying its geometric origin.

Findings

Closed-form third-order polynomial action with a single cubic interaction

Elimination of the need for a special gauge in the formulation

Emergence of geometric interpretation from the derivation

Abstract

We present a non-geometric derivation of $\mathcal{N}$=1 Super Yang-Mills by focusing on the consistency of interactions that extend the free vector supermultiplet rather than assuming gauge invariance under extended symmetries. By utilizing a superspace first-order description, the theory is given in closed form as a third-order polynomial which includes a single cubic interaction term instead of an infinite series, thus eliminating the need for a special gauge. The geometrical interpretation of the theory emerges, as opposed to being presupposed.