Linear Versus Non-linear Supersymmetry, in General

TL;DR

This paper explores superconformal and supergravity models with constrained superfields, demonstrating how linear supersymmetry can be transformed into non-linear forms through equations of motion for Lagrange multiplier superfields.

Contribution

It provides a comprehensive framework for understanding the transition from linear to non-linear supersymmetry in models with various constrained superfields, including the derivation of exact non-linear forms.

Findings

All unconstrained superfields with linear supersymmetry can be constrained via Lagrange multipliers.

The exact non-linear supersymmetry transformations are derived from the original linear models.

Examples include chiral, linear, and complex superfields with various multiplet spins.

Abstract

We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM's: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.