Properties of Nilpotent Supergravity

TL;DR

This paper develops supergravity models with a goldstino multiplet originating from gravitational fields, exploring their dualities, matter couplings, and applications to inflationary models.

Contribution

It introduces a novel supergravity framework where the goldstino has a gravitational origin and analyzes its implications for matter couplings and inflation.

Findings

Duality to the Volkov-Akulov Lagrangian confirmed

Restricted matter couplings due to gravitational origin

Explicit inflationary models constructed

Abstract

We construct Supergravity models where the goldstino multiplet has a gravitational origin, being dual to the chiral curvature superfield. Supersymmetry is nonlinearly realized due to a nilpotent constraint, while the goldstino arises from $\gamma$-traces of the gauge-invariant gravitino field strength. After duality transformations one recovers, as expected, the standard Volkov-Akulov Lagrangian coupled to Supergravity, but the gravitational origin of the goldstino multiplet restricts the available types of matter couplings. We also construct explicitly some inflationary models of this type, which contain both the inflaton and the nilpotent superfield.