On commutator-based linearization of vector-spinor nonlinear supersymmetry and Rarita-Schwinger fields

We discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both \(N = 1\) and \(N\)-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of spin-3/2 Nambu-Goldstone (NG) fermions, which are expressed as...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Author: Tsuda, Motomu
Format: Article
Language:English
Subjects:
Commutators
Fermions
Gauge invariance
Linearization
Supersymmetry
Online Access:Get full text
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Summary:We discuss the linearization of vector-spinor (spin-3/2) nonlinear supersymmetry (vsNLSUSY) transformations for both \(N = 1\) and \(N\)-extended SUSY in flat spacetime based on the commutator algebra by using functionals (composites) of spin-3/2 Nambu-Goldstone (NG) fermions, which are expressed as simple products of powers of the spin-3/2 NG fermions and a fundamental determinant in the vsNLSUSY theory. We define basic component fields by means of those functionals in a linearized vsSUSY theory including spin-3/2 fields, general auxiliary ones and a \(D\)-term. The general forms of linear (rigid) vsSUSY transformations for the component fields are determined uniquely from the commutator-based linearization procedure. By considering appropriate recombinations of the functionals of the spin-3/2 NG fermions for \(N = 1\) SUSY, we find that variations of the recombinations under the vsNLSUSY transformations include linear spin-1/2 SUSY ones of spin-(3/2, 1) fields with \(U(1)\) gauge invariance. The spinorial gauge invariance of the Rarita-Schwinger action in the linearization process is also discussed together with the \(U(1)\) gauge invariance.
ISSN:2331-8422
DOI:10.48550/arxiv.2203.08443