Relating the Komargodski-Seiberg and Akulov-Volkov actions: Exact nonlinear field redefinition

TL;DR

This work constructs an exact nonlinear field redefinition that maps the Akulov-Volkov action to the Komargodski-Seiberg Goldstino action, establishing a concrete link between two realizations of spontaneously broken supersymmetry. By analyzing the mapping order by order in the coupling $\kappa$, the authors determine constraints on the redefinition parameters, derive the inverse transformation, and show that 12 real degrees of freedom correspond to symmetry redundancies that can be set to zero to yield a compact form. The construction confirms the relation $2f^2=\kappa^{-2}$ between KS and AV parameters and provides an explicit $\delta_\xi\psi$ transformation for the KS action obtained via the map. The paper also argues that certain alternative derivations (arXiv:1003.4143v2, arXiv:1009.2166) are inconsistent, and discusses the inconsistency in Zheltukhin's four-component approach, thereby clarifying the correct nonlinear SUSY structure.

Abstract

This paper constructs an exact field redefinition that maps the Akulov-Volkov action to that recently studied by Komargodski and Seiberg in arXiv:0907.2441. It is also shown that the approach advocated in arXiv:1003.4143v2 and arXiv:1009.2166 for deriving such a relationship is inconsistent.