No Supersymmetry without Supergravity: Induced Supersymmetry Representations on Composite Effective Fields

TL;DR

This paper investigates how induced supersymmetry representations on composite operators influence the formulation of effective actions, especially in N=1 SYM, revealing constraints and the necessity of including superconformal currents in supergravity backgrounds.

Contribution

It demonstrates that effective actions involving composite operators must accommodate non-linear supersymmetry representations and includes superconformal currents in the analysis of N=1 SYM with soft breaking.

Findings

Induced supersymmetry representations lead to constraints on effective action formulations.

In N=1 SYM, soft supersymmetry breaking requires including superconformal currents.

Effective actions must be consistent with non-linear supersymmetry representations.

Abstract

Induced supersymmetry representations on composite operators are studied. In superspace the ensuing transformation rules (trivially) lead to an effective superfield. On the other hand, an induced representation must exist for non-linear (``on-shell'') supersymmetry as well. As this choice of the representation is physically irrelevant, any formulation of an effective action starting from the superspace representation must equally well be possible in a non-linear representation. We show that this leads to very relevant constraints on the formulation of effective actions in terms of composite operators. These ideas are applied to the simplest case of such a theory, N=1 SYM. It is shown that soft supersymmetry breaking within that theory forces one to include besides the Lagrangian multiplet S all currents of the super-conformal structure, embedded in a supergravity background, as relevant fields.