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

Abstract

Recently Kuzenko and McCarty observed the cancellation of 4-derivative terms in the $D=4\mathcal{N}=1$ 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.

18 pages; the version accepted for publication in Phys. Rev. D; new section regarding the proof of the equivalence between the Komargodski-Seiberg and the Volkov-Akulov actions is added: some comments and new references are included

References in corpus (6)

• From Linear SUSY to Constrained Superfields
• Non-linear MSSM
• Goldstinos, Supercurrents and Metastable SUSY Breaking in N=2 Supersymmetric Gauge Theories
• Leading-Order Actions of Goldstino Fields
• On the cancellation of 4-derivative terms in the Volkov-Akulov action
• Dmitrij Volkov, super-Poincare group and Grassmann variables

Cited by in corpus (7)

• Relating the Komargodski-Seiberg and Akulov-Volkov actions: Exact nonlinear field redefinition
• On the Goldstino actions and their symmetries
• Leading-Order Actions of Goldstino Fields
• On equivalence of the Komargodski-Seiberg action to the Volkov-Akulov action
• On the cancellation of 4-derivative terms in the Volkov-Akulov action
• Linear space of spinor monomials and realization of the Nambu-Goldstone fermion in the Volkov-Akulov and Komargodski-Seiberg Lagrangians
• Identities in Nonlinear Realizations of Supersymmetry