Some systematics in the relation between linear and nonlinear global supersymmetry in curved spacetime

TL;DR

This paper explores the systematic linearization of nonlinear supersymmetry in curved spacetime within the superon-graviton model, aiming to connect nonlinear and linear SUSY formulations in a supergravity context.

Contribution

It introduces a method to linearize N=1 nonlinear supersymmetry in curved spacetime using modified superspace translations and transformations, advancing the understanding of SUSY relations.

Findings

Homogeneous transformation law of superfields established

Constraints on torsion and Lorentz parameters identified

Preliminary supermultiplet construction discussed

Abstract

We focus on a nonlinear supersymmetry (NL SUSY) in curved spacetime introduced in the superon-graviton model (SGM) towards a SUSY composite unified model based on SO(10) super-Poincar\'e symmetry, and we consider for $N = 1$ SUSY a systematic procedure to linearize the NL SUSY. By introducing modified superspace translations of superspace coordinates and their specific coordinate transformations both depending on a Nambu-Goldstone fermion, we show a homogeneous transformation's law of superfields which is important in the relation between linear (L) and NL SUSY. Furthermore, as a preliminary to find a L supermultiplet which is equivalent to the $N = 1$ NL SUSY SGM multiplet, we discuss on the realization of the modified superspace translations in the construction of a supergravity-like multiplet in the superspace formalism. In particular, we find constraints on a torsion and a Lorentz transformation parameter in the superspace formalism to realize the modified supertranslations.