Nilpotent ${\cal N}=1$ tensor multiplet

TL;DR

This paper introduces a new nilpotent ${ m N}=1$ tensor multiplet in supersymmetry, describing Goldstino and axion fields, with formulations in supergravity contexts, expanding the toolkit for supersymmetric model building.

Contribution

It presents a novel nilpotent ${ m N}=1$ tensor multiplet using a deformed real linear superfield with cubic nilpotency, and explores its couplings to super Yang-Mills and supergravity.

Findings

Defines a nilpotent tensor multiplet with Goldstino and axion fields.

Provides formulations in both global and local supersymmetry frameworks.

Establishes couplings to super Yang-Mills and supergravity theories.

Abstract

We propose a nilpotent ${\cal N}=1$ tensor multiplet describing two fields, which are the Goldstino and the axion, the latter being realised in terms of the field strength of a gauge two-form. This supersymmetric multiplet is formulated in terms of a deformed real linear superfield, subject to a cubic nilpotency condition. Its couplings to a super Yang-Mills multiplet and supergravity are presented. To define a nilpotent tensor multiplet in the locally supersymmetric case, one has to make use of either real or complex three-form supergravity theories, which are variant realisations of the old minimal formulation for ${\cal N}=1$ supergravity.