# On curvature-squared invariants of minimal five-dimensional supergravity from superspace

## TL;DR

This paper develops an off-shell superspace framework for curvature-squared invariants in five-dimensional supergravity, providing explicit formulas and equations of motion, advancing the understanding of higher-derivative supergravity theories.

## Contribution

It introduces explicit expressions for invariants and equations of motion in five-dimensional supergravity with higher derivatives, using superspace methods and compensator multiplets.

## Key findings

- Explicit linear multiplet expression based on a prepotential.
- Primary equations of motion for deformed supergravity.
- Identification of a new four-derivative invariant for scalar curvature squared.

## Abstract

We elaborate on the off-shell superspace construction of curvature-squared invariants in minimal five-dimensional supergravity. This is described by the standard Weyl multiplet of conformal supergravity coupled to two compensators being a vector multiplet and a linear multiplet. In this set-up, we review the definition of the off-shell two-derivative gauged supergravity together with the three independent four-derivative superspace invariants defined in arXiv:1410.8682. We provide the explicit expression for the linear multiplet based on a prepotential given by the logarithm of the vector multiplet primary superfield. We then present for the first time the primary equations of motion for minimal gauged off-shell supergravity deformed by an arbitrary combination of these three four-derivative locally superconformal invariants. We also identify a four-derivative invariant based on the linear multiplet compensator and the kinetic superfield of a vector multiplet which can be used to engineer an alternative supersymmetric completion of the scalar curvature squared.