On the linearization of nonlinear supersymmetry based on the commutator algebra

TL;DR

This paper presents a method to linearize nonlinear supersymmetry by analyzing the closure of the commutator algebra, explicitly deriving linear SUSY transformations for vector supermultiplets from Nambu-Goldstone fermions.

Contribution

It introduces a systematic linearization procedure of NLSUSY based on the commutator algebra, explicitly deriving linear SUSY transformations for vector supermultiplets.

Findings

Linear SUSY transformations are uniquely determined from the commutator algebra.

The method applies to functionals of Nambu-Goldstone fermions and their derivatives.

Explicit derivation of vector supermultiplet transformations from NLSUSY.

Abstract

We discuss a linearization procedure of nonlinear supersymmetry (NLSUSY) based on the closure of the commutator algebra for variations of functionals of Nambu-Goldstone fermions and their derivative terms under NLSUSY transformations in Volkov-Akulov NLSUSY theory. In the case of a set of bosonic and fermionic functionals, which leads to (massless) vector linear supermultiplets, we explicitly show that general linear SUSY transformations of basic components defined from those functionals are uniquely determined by examining the commutation relation in the NLSUSY theory.