Incompatibility of simultaneous non-linear realizations of scale symmetry and supersymmetry

TL;DR

This paper demonstrates that simultaneous nonlinear realizations of supersymmetry and scale symmetry are incompatible because the Goldstino decay constant must vanish in the chiral limit, making such realizations inconsistent.

Contribution

It shows that the simultaneous nonlinear realization of supersymmetry and scale symmetry cannot be achieved due to the dependence of the Goldstino decay constant on soft breaking parameters.

Findings

Goldstino decay constant varies with soft breaking parameters

Incompatibility of nonlinear realizations of supersymmetry and scale symmetry

Decay constant must vanish in the chiral limit

Abstract

Simultaneous nonlinear realizations of supersymmetry and softly broken scale and chiral symmetries are investigated. To guarantee Nambu-Goldstone realizations of the symmetries, the Goldstino decay constant is forced to vary as the explicit soft scale and chiral symmetry breaking parameters. Consequently, it must vanish in the chiral limit and the simultaneous nonlinear realizations of the super and scale symmetries proves inconsistent.