${\cal R}^2$ Supergravity

TL;DR

This paper formulates a scale-invariant $R^2$ supergravity theory using superfields, explores its duals in different minimal formulations, and reveals a novel extension of the Freedman model with implications for de Sitter space.

Contribution

It introduces a superfield-based formulation of $R^2$ supergravity and uncovers its dual descriptions, including a new extension of the Freedman model in de Sitter space.

Findings

Dual theories in old and new minimal formulations are derived.

The new minimal dual extends the Freedman model with a massless gauge and chiral multiplet.

The inverse radius relates to the Fayet-Iliopoulos term, indicating a de-Higgsed phase.

Abstract

We formulate $R^2$ pure supergravity as a scale invariant theory built only in terms of superfields describing the geometry of curved superspace. The standard supergravity duals are obtained in both "old" and "new" minimal formulations of auxiliary fields. These theories have massless fields in de Sitter space as they do in their non supersymmetric counterpart. Remarkably, the dual theory of $R^2$ supergravity in the new minimal formulation is an extension of the Freedman model, describing a massless gauge field and a massless chiral multiplet in de Sitter space, with inverse radius proportional to the Fayet-Iliopoulos term. This model can be interpreted as the "de-Higgsed" phase of the dual companion theory of $R+R^2$ supergravity.