All unitary cubic curvature gravities in D dimensions

TL;DR

This paper systematically constructs all unitary cubic curvature gravity theories in D dimensions, simplifying the complex problem of propagator analysis by using equivalent quadratic actions and classifying unitary quadratic models.

Contribution

It provides a comprehensive classification of unitary cubic curvature gravity theories in arbitrary dimensions and analyzes their properties using equivalent quadratic actions.

Findings

Classified all unitary quadratic models in D dimensions.

Constructed all unitary cubic curvature gravity theories in (A)dS backgrounds.

Analyzed the scattering and extensions of critical gravity.

Abstract

We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D -dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.