Ghost-free, finite, fourth order D=3 (alas) gravity

TL;DR

This paper analyzes a specific three-dimensional gravity model, demonstrating its ghost-free, finite, and conformal-invariant properties, and clarifying its relation to second-order scalar-tensor theories.

Contribution

It provides a canonical analysis of a novel 3D gravity model, showing its pure quadratic branch is ghost-free, finite, and conformally invariant, and clarifies its irreducible fourth-order nature.

Findings

The pure quadratic branch is ghost-free and massless.

The model is power-counting UV finite.

The pure quadratic branch is irreducibly fourth-order.

Abstract

Canonical analysis of a recently proposed [1] linear+quadratic curvature gravity model in D=3 displays its pure fourth derivative quadratic branch as a ghost-free (massless) excitation. Hence it both negates an old no-go theorem and is power-counting UV finite. It is also conformal-invariant, so the metric is underdetermined. While the 2-term branch is also ghost-free, it has, as shown in [1], a second-derivative, two-tensor equivalent, akin to the second order scalar-tensor form of ostensibly fourth order, $R+R^2$, actions. This correspondence fails for the pure quadratic branch: it is irreducibly fourth-order.