Non-linearly ghost-free higher curvature gravity

TL;DR

This paper develops ghost-free higher curvature gravity theories in the vielbein formalism, establishing their equivalence to massive bigravity, and explores their properties and implications in three and four dimensions, including unitarity and torsion effects.

Contribution

It introduces new ghost-free higher curvature gravity models in the vielbein formalism, connecting them to massive bigravity and analyzing their features in various dimensions.

Findings

In 3D, quadratic gravity is equivalent to zwei-dreibein gravity and ghost-free.

In 4D, ghost-free models require infinite higher curvature terms.

Unitarity in AdS/CFT implies non-vanishing torsion in the bulk.

Abstract

We find unitary and local theories of higher curvature gravity in the vielbein formalism, known as the Poincar\'{e} gauge theory by utilizing the equivalence to the ghost-free massive bigravity. We especially focus on three and four dimensions but extensions into a higher dimensional spacetime are straightforward. In three dimensions, a quadratic gravity $\mathcal{L}=R+T^2+R^2$, where $R$ is the curvature and $T$ is the torsion with indices omitted, is shown to be equivalent to zwei-dreibein gravity and free from the ghost at fully non-linear orders. In a special limit, new massive gravity is recovered. When the model is applied to the AdS/CFT correspondence, unitarity both in the bulk theory and in the boundary theory implies that the torsion must not vanish. On the other hand, in four dimensions, the absence of ghost at non-linear orders requires an infinite number of higher curvature terms, and these terms can be given by a schematic form $R(1+R/\alpha m^2)^{-1}R$ where $m$ is the mass of the massive spin-2 mode originating from the higher curvature terms and $\alpha$ is an additional parameter that determines the amplitude of the torsion. We also provide another four-dimensional ghost-free higher curvature theory that contains a massive spin-0 mode as well as the massive spin-2 mode.