On Unitarity of Massive Gravity in Three Dimensions

TL;DR

This paper investigates the unitarity of a higher-derivative massive gravity model in three dimensions, confirming its unitarity at tree level and showing non-unitarity issues in higher dimensions due to massless modes.

Contribution

It demonstrates the unitarity of a specific higher-derivative massive gravity model in three dimensions and analyzes the challenges of extending it to higher dimensions.

Findings

Model is unitary in three dimensions at tree level

Higher dimensions introduce non-unitary massless spin-2 modes

Extension to higher dimensions faces fundamental unitarity issues

Abstract

We examine a unitarity of a particular higher-derivative extension of general relativity in three space-time dimensions, which has been recently shown to be equivalent to the Pauli-Fierz massive gravity at the linearized approximation level, and explore a possibility of generalizing the model to higher space-time dimensions. We find that the model in three dimensions is indeed unitary in the tree-level, but the corresponding model in higher dimensions is not so due to the appearance of non-unitary massless spin-2 modes.