The Goldstino Field in Linear and Nonlinear Realizations of Supersymmetry

TL;DR

This paper demonstrates how to construct a Goldstino field within nonlinear supersymmetry from linear models, showing the reformulation process and the Goldstino's role in the transformed Lagrangian.

Contribution

It provides a method to derive nonlinear supersymmetric models from linear theories using a chiral super-multiplet, clarifying the Goldstino's emergence and behavior.

Findings

Goldstino constructed from linear models in nonlinear realization

Goldstino appears in Jacobian and derivatives after transformation

Vertices with Goldstino involve at least one space-time derivative

Abstract

A Goldstino field in the nonlinear realization of supersymmetry is constructed from an appropriate chiral super-multiplet of the linear theory, in general O'Raifeataigh-like models. The linear theories can thus be reformulated into their nonlinear versions, via the standard procedure. The Goldstino field disappears totally from the original Lagrangian in the process, but reemerges in the Jacobian of the transformation and covariant derivatives. Vertices with Goldstino fields carry at least one space-time derivative, as one would have expected.