Identities in Nonlinear Realizations of Supersymmetry

TL;DR

This paper explores the duality between linear and nonlinear realizations of supersymmetry breaking, revealing identities involving Goldstino and matter fields that ensure the uniqueness of the nonlinear Kähler potential.

Contribution

It identifies subtle identities linking linear and nonlinear SUSY realizations, demonstrating the uniqueness of the nonlinear Kähler potential through total-divergence analysis.

Findings

Identified identities involving Goldstino and matter fields in nonlinear SUSY.

Proved the uniqueness of the nonlinear Kähler potential when the linear one is fixed.

Showed that complex integrands in nonlinear realization are total divergences.

Abstract

In this paper, we emphasize that a UV SUSY-breaking theory can be realized either linearly or nonlinearly. Both realizations form the dual descriptions of the UV SUSY-breaking theory. Guided by this observation, we find subtle identities involving the Goldstino field and matter fields in the standard nonlinear realization from trivial ones in the linear realization. Rather complicated integrands in the standard nonlinear realization are identified as total-divergences. Especially, identities only involving the Goldstino field reveal the self-consistency of the Grassmann algebra. As an application of these identities, we prove that the nonlinear Kahler potential without or with gauge interactions is unique, if the corresponding linear one is fixed. Our identities pick out the total-divergence terms and guarantee this uniqueness.