On a possible new R^2 theory of supergravity

TL;DR

This paper introduces a new R^2-type supergravity theory based on the superalgebra Osp(1|8), exploring its symmetry invariances and algebraic structure, extending conformal supergravity with novel constraints.

Contribution

It proposes a novel supergravity model using an R^2-type action and analyzes its gauge symmetries and algebraic closure, extending existing conformal supergravity frameworks.

Findings

Invariance under certain local symmetries is achieved with specific curvature constraints.

Symmetries with positive Weyl weight require further modifications for invariance.

The gauge algebra closure analysis supports the proposed symmetry structure.

Abstract

We consider a new MacDowell-Mansouri R^2-type of supergravity theory, an extension of conformal supergravity, based on the superalgebra Osp(1|8). Invariance under local symmetries with negative Weyl weight is achieved by imposing chirality-duality and double-duality constraints on curvatures, along with the usual constraint of vanishing supertorsion. An analysis of the remaining gauge symmetries shows that those with vanishing Weyl weight are invariances of the action at the linearized level. For the symmetries with positive Weyl weight we find that invariance of the action would require further modifications of the transformation rules. This conclusion is supported by a kinematical analysis of the closure of the gauge algebra.