Commutator-based linearization of $N = 1$ nonlinear supersymmetry

TL;DR

This paper presents a method to linearize N=1 nonlinear supersymmetry using a commutator algebra, deriving various supermultiplets from fundamental functionals related to Nambu-Goldstone fermions.

Contribution

It introduces a novel approach to linearize N=1 NLSUSY via commutator algebra, unifying the derivation of multiple supermultiplets from basic composites.

Findings

Supermultiplets are obtained from a common set of bosonic and fermionic functionals.

These functionals are expressed as products of Nambu-Goldstone fermions and a fundamental determinant.

The approach explicitly connects nonlinear and linear SUSY formulations.

Abstract

We consider the linearization of $N = 1$ nonlinear supersymmetry (NLSUSY) based on a commutator algebra in Volkov-Akulov NLSUSY theory. We show explicitly that $U(1)$ gauge and scalar supermultiplets in addition to a vector supermultiplet with general auxiliary fields in linear SUSY theories are obtained from a same set of bosonic and fermionic functionals (composites) which are expressed as simple products of the powers of a Nambu-Goldstone fermion and a fundamental determinant in the NLSUSY theory.