Unavoidable Conflict Between Massive Gravity Models and Massive Topological Terms

TL;DR

This paper demonstrates that adding massive topological terms to certain 2+1 dimensional massive gravity models causes unitarity issues, revealing a fundamental conflict contrary to previous beliefs.

Contribution

It shows that the coexistence of massive gravity models and massive topological terms in 2+1 dimensions is inherently incompatible due to unitarity violations.

Findings

Massive gravity models are unitary at tree level without topological terms.

Adding Chern-Simons terms spoils unitarity in these models.

Nonunitary behavior persists when combining higher-derivative gravity with topological terms.

Abstract

Massive gravity models in 2+1 dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar squared ($R^2$), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern-Simons term. Furthermore, if the massive topological term is added to $R + R_{\mu\nu}^2$ gravity, or to $R + R_{\mu\nu}^2 + R^2$ gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.