Leading-Order Actions of Goldstino Fields

TL;DR

This paper analyzes the leading-order Goldstino actions, comparing the Akulov-Volkov action with the constrained superfield formalism, and clarifies their relationships and equivalence in terms of S-matrix elements.

Contribution

It provides explicit expressions for the Akulov-Volkov actions and clarifies how different formulations relate and produce equivalent physical results.

Findings

S_KS and S_AV/S_AV^ch yield the same S-matrix elements

Explicit expressions for S_AV and S_AV^ch are presented

The relationship between different Goldstino actions is clarified

Abstract

This paper starts with a self-contained discussion of the so-called Akulov-Volkov action S_AV, which is traditionally taken to be the leading-order action of Goldstino field. Explicit expressions for S_AV and its chiral version S_AV^ch are presented. We then turn to the issue on how these actions are related to the leading-order action S_NL proposed in the newly proposed constrained superfield formalism. We show that S_NL may yield S_AV/S_AV^ch or a totally different action S_KS, depending on how the auxiliary field in the former is integrated out. However, S_KS and S_AV/S_AV^ch always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory.