On the role of the commutator algebra for nonlinear supersymmetry

TL;DR

This paper explores how the algebra of commutators in nonlinear supersymmetry (NLSUSY) influences the structure and transformations of supermultiplets, both in flat and curved spacetime, highlighting its importance in extended SUSY.

Contribution

It demonstrates that variations of functionals in NLSUSY uniquely determine linear SUSY transformations for vector supermultiplets, emphasizing the role of commutator algebra closure.

Findings

Closure of commutator algebra is crucial for defining SUSY transformations.

Variations of functionals determine linear SUSY transformations.

The role of NLSUSY algebra is essential in extended SUSY theories.

Abstract

We discuss a closure of commutator algebras for general functionals in terms of Nambu-Goldstone fermions and their derivative terms under nonlinear supersymmetry (NLSUSY) both in flat spacetime and in curved spacetime. We point out that variations of functionals for vector supermultiplets (uniquely) determine general LSUSY transformations for linear vector supermutiplets with general auxiliary fields in extended SUSY, where the closure of the commutator algebras for NLSUSY plays a crucial role.