Nilpotent mathcal{N}=1 tensor multiplet

Sergei M Kuzenko

doi:10.1007/jhep04(2018)131

Abstract

We propose a nilpotent mathcal{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 mathcal{N}=1 supergravity.

Highlights

We propose a nilpotent 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
JHEP04(2018)131 positive contribution to the cosmological constant, which is associated with the Goldstino

Summary

A generalisation of the linear-chiral duality

We start by recalling the linear-chiral duality as described in [37]. Consider a general two-derivative model for a self-interacting N = 1 tensor multiplet [30]. Where FD is the Legendre transform of F. where FD is the Legendre transform of F This supersymmetric nonlinear σ-model is a dual formulation for the tensor multiplet theory (2.1). There exists a variant realisation of the scalar multiplet known as the three-form multiplet [39]. It is obtained by replacing the chiral scalar Φ with χ given by χ = − 1 D 2U , 4. Starting from the nonlinear σ-model (2.4), we may construct a theory of selfinteracting three-form multiplet. Sα[K, χ, χ] = d4xd2θd2θ F (K) − (eiαχ + e−iαχ)K This equation defines a deformed real linear multiplet

New nilpotent multiplet

Nilpotent tensor multiplet coupled to a three-form multiplet

Coupling to three-form supergravity

A More duality transformations