A Study of Two-/One-form Superfields

TL;DR

This paper investigates two simplified supersymmetric models involving 1- and 2-form superfields, demonstrating their complete off-shell solvability, constrained kinematics, and rigid supersymmetry representations, with implications for gauge theory algebra structures.

Contribution

It introduces and analyzes two toy models of k-form superfields, revealing their solvability and algebraic properties, advancing understanding of supersymmetry in gauge theories.

Findings

Models are completely solvable off-shell.

Models exhibit severely constrained kinematics.

Models form rigid supersymmetry representations.

Abstract

We study two supersymmetric toy models of a k-form superfield, k=2,1 separately. By ``solving'' Jacobi identities, we show that each model is completely solvable at off-shell level, possesses a severely constrained kinematics, and gives a rigid representation of the supersymmetry algebra. This study of the toy models is motivated by our reanalysis on supersymmetry algebras in gauge theories where we discuss internal symmetry generators carrying spacetime/spinor indices.