Linearizing N = 3 nonlinear supersymmetry in two dimensions

TL;DR

This paper explores the algebraic relationship between nonlinear and linear N=3 supersymmetry in two dimensions, demonstrating their equivalence and analyzing the role of auxiliary fields and spontaneous SUSY breaking.

Contribution

It derives SUSY-invariant relations connecting the VA nonlinear model to a linear supermultiplet and discusses the compatibility of different SO(3) representations in the linearization process.

Findings

Established algebraic relations between NL and linear SUSY models

Demonstrated equivalence of VA action to a free linear SUSY action with FI D term

Showed compatibility of different SO(3) representations in the same massless state

Abstract

We investigate for N = 3 supersymmetry (SUSY) in D = 2 the algebraic relation between the Volkov-Akulov (VA) model of nonlinear (NL) SUSY and a (renormalizable) SO(3) vector supermultiplet of linear (L) SUSY. We derive SUSY and SO(3) invariant relations between component fields of the vector supermultiplet and Nambu-Goldstone (NG) fermions of the VA model at leading orders by using three arbitrary dimensionless parameters which can be recasted as the vacuum expectation values of auxiliary fields in the vector supermultiplet. Two different irreducible representations of SO(3) super-Poincar\'e symmetry which appear in the same massless state are compatible with each other in the linearization of NL SUSY. The equivalence of a NL SUSY VA action to a free L SUSY action containing the Fayet-Iliopoulos (FI) D term which indicates a spontaneously SUSY breaking is also discussed explicitly according to the SUSY invariant relations.