Three-form multiplet and supersymmetry breaking

Abstract

Recently, a nilpotent real scalar superfield $V$ was introduced in arXiv:1702.02423 as a model for the Goldstino. It contains only two independent component fields, the Goldstino and the auxiliary $D$-field. Here we first show that $V$ can equivalently be realised as a constrained three-form superfield. We demonstrate that every irreducible Goldstino superfield (of which the Goldstino is the only independent component field) can be realised as a descendant of $V$ which is invariant under local rescalings $V\to {\mathrm{e}}^{\tau }V$, where $\tau$ is an arbitrary real scalar superfield. We next propose a new Goldstino supermultiplet which is described by a nilpotent three-form superfield $\mathcal{Y}$ that is a variant formulation for the nilpotent chiral superfield, which is often used in off-shell models for spontaneously broken supergravity. It is shown that the action describing the dynamics of $\mathcal{Y}$ may be obtained from a supersymmetric nonlinear $\sigma$-model in the infrared limit. Unlike $V$, the Goldstino superfield $\mathcal{Y}$ contains two independent auxiliary fields, $F=H+\mathrm{i}G$, of which $H$ is a scalar and $G$ is the field strength of a gauge three-form. When $\mathcal{Y}$ is coupled to supergravity, both $H$ and $G$ produce positive contributions to the cosmological constant. While the contribution from $H$ is uniquely determined by the parameter of the supersymmetry breaking in the action, the contribution from $G$ is dynamical.

18 pages; minor corrections

References in corpus (4)

• From Linear SUSY to Constrained Superfields
• The Goldstino Brane, the Constrained Superfields and Matter in N=1 Supergravity
• Scanning of the Supersymmetry Breaking Scale and the Gravitino Mass in Supergravity
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Cited by in corpus (15)

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• Three-forms, dualities and membranes in four-dimensional supergravity
• Complex three-form supergravity and membranes
• Three-forms, Supersymmetry and String Compactifications
• New nilpotent $\mathcal{N}=2$ superfields
• Higher derivative three-form gauge theories and their supersymmetric extension
• On the dynamical origin of parameters in $\mathcal{N}=2$ Supersymmetry
• Two-form supergravity, superstring couplings, and Goldstino superfields in three dimensions
• Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories
• Higher Forms and Membranes in 4D Supergravities
• Three-forms and Fayet-Iliopoulos terms in Supergravity: Scanning Planck mass and BPS domain walls
• Non-supersymmetric branes
• de Sitter decay through goldstino evaporation
• Nilpotent $\mathcal{N}=1$ tensor multiplet
• Goldstino superfields in supergravity