Linearizing extended nonlinear supersymmetry in two dimensional spacetime

TL;DR

This paper develops a method to linearize nonlinear supersymmetry in two-dimensional spacetime, specifically for extended SUSY theories, by deriving transformations of component fields from NG fermion composites.

Contribution

It provides a systematic approach to linearize extended nonlinear supersymmetry in 2D, explicitly constructing component fields and transformations from NG fermion functionals.

Findings

Explicit linear SUSY transformations derived from NG fermion composites.

Transition mechanisms between vector and U(1) gauge supermultiplets shown.

Applicable to N=2 and N=3 extended SUSY theories in 2D.

Abstract

We linearize nonlinear supersymmetry in the Volkov-Akulov (VA) theory for extended SUSY in two dimensional spacetime ($d = 2$) based on the commutator algebra. Linear SUSY transformations of basic component fields for general vector supermultiplets are uniquely determined from variations of functionals (composites) of Nambu-Goldstone (NG) fermions, which are represented as simple products of powers of the NG fermions and a fundamental determinant in the VA theory. The structure of basic component fields with general auxiliary fields in the vector supermultiplets and transitions to $U(1)$ gauge supermultiplets through recombinations of the functionals of the NG fermions are explicitly shown both in $N = 2$ and $N = 3$ theories as the simplest and general examples for extended SUSY theories in $d = 2$.