Linearizing N = 1 nonlinear supersymmetry with higher derivative terms of a Nambu-Goldstone fermion

TL;DR

This paper explores the connection between linear and nonlinear N=1 supersymmetry models involving higher derivative terms of a Nambu-Goldstone fermion, demonstrating their equivalence despite apparent pathologies.

Contribution

It constructs SUSY invariant relations with higher derivatives linking linear and nonlinear SUSY models, and proves their equivalence including models with higher derivative pathologies.

Findings

Established SUSY invariant relations with higher derivatives

Proved equivalence between standard and higher derivative NL SUSY models

Demonstrated universality of NL SUSY actions with N-G fermions

Abstract

We investigate for N = 1 supersymmetry (SUSY) the relation between a scalar supermultiplet of linear SUSY and a nonlinear (NL) SUSY model including apparently pathological higher derivaive terms of a Nambu-Goldstone (N-G) fermion besides the Volkov-Akulov (V-A) action. SUSY invariant relations with higher derivative terms of the N-G fermion, which connect the linear and NL SUSY models, are constructed at leading orders by heuristic arguments. We discuss a higher derivative action of the N-G fermion in the NL SUSY model, which apparently includes a (Weyl) ghost field. By using this relation, we also explicitly prove an equivalence between the standard NL SUSY V-A model and our NL SUSY model with the pathological higher derivatives as an example with respect to the universality of NL SUSY actions with the N-G fermion.