On the cancellation of 4-derivative terms in the Volkov-Akulov action

TL;DR

This paper provides an algebraic proof of the cancellation of 4-derivative terms in the Volkov-Akulov action, highlighting differences with related superfield actions and establishing equivalence up to first order.

Contribution

It offers a simple algebraic proof of 4-derivative term cancellation in the VA action using Majorana bispinors and Fierz identities, clarifying its relation to other supersymmetric actions.

Findings

Cancellation of 4-derivative terms in VA action confirmed

Difference between VA and superfield actions identified

Equivalence between KS and VA Lagrangians established at first order

Abstract

Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms in the $D=4 {\cal N}=1$ Volkov-Akulov supersymmetric action for the fermionic Nambu-Goldstone field. Here is presented a simple algebraic proof of the cancellation based on using the Majorana bispinors and Fiertz identities. The cancellation shows a difference between the Volkov-Akulov action and the effective superfield action recently studied by Komargodski and Seiberg and containing one 4-derivative term. We find out that the cancellation effect takes place in coupling of the Nambu-Goldstone fermion with the Dirac field. Equivalence between the KS and the VA Lagrangians is proved up to the first order in the interaction constant of the NG fermions.