No Supersymmetry without Supergravity Induced Supersymmetry Representations on Composite Effective Superfields

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. PACS: 11.15.Kc; 11.30.Pb; 11.30.Qc keywords: SYM theory; non-linear representations; low-energy effective action email: bergamin@tph.tuwien.ac.at, phone: +43 1 58801 13622, fax: +43 1 58801 13699 email: mink@itp.unibe.ch, phone: +41 31 631 8624, fax: +41 31 631 3821

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