Linearizing extended nonlinear supersymmetry in two dimensional spacetime

Motomu Tsuda

doi:10.1016/j.nuclphysb.2018.11.013

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.

Highlights

Relations between Volkov-Akulov (VA) nonlinear supersymmetric (NLSUSY) theory [1] and linear SUSY (LSUSY) ones [2, 3] are shown explicitly for N = 1 and N = 2 SUSY theories [4]-[8]
We have recently proposed a linearization procedure of NLSUSY based on a commutator algebra in the VA NLSUSY theory [10] by introducing a set of fermionic and bosonic functionals which are represented as products of powers of the NG fermions and a fundamental determinant indicating a spontaneous SUSY breaking in the VA NLSUSY action
We focus on the VA NLSUSY theory for extended SUSY in d = 2 and apply the commutator-based linearization procedure to it since explicit calculations for the d = 2 NL/LSUSY relation give many suggestive and significant results to d = 4 SUSY theories as for the structure of the functionals of the NG fermions for vector supermultiplets [15] and SUSY models with interaction terms [16]-[18] etc

Summary

Introduction

We have recently proposed a linearization procedure of NLSUSY based on a commutator algebra in the VA NLSUSY theory [10] by introducing a set of fermionic and bosonic functionals which are represented as products of powers of the NG fermions and a fundamental determinant indicating a spontaneous SUSY breaking in the VA NLSUSY action In this linearization method, variations of basic components defined from the above set of the functionals under the NLSUSY transformations uniquely determine LSUSY transformations for (massless) vector supermultiplets.

Functionals of Nambu-Goldstone fermions for vector supermultiplets

Gζ1 α13

M ijj 2

Summary and discussions