Unitarity versus Renormalizability of Higher Derivative Gravity in 3D

TL;DR

This paper investigates the renormalizability of three-dimensional higher derivative gravity theories, showing that generic quadratic curvature theories are renormalizable, while specific models like new massive gravity are not.

Contribution

It clarifies the conditions under which 3D higher derivative gravity theories are renormalizable, distinguishing between generic and special coefficient relations.

Findings

Generic quadratic curvature theories in 3D are renormalizable.

New massive gravity with special coefficient relations is not renormalizable.

The study provides criteria for renormalizability in 3D higher derivative gravity.

Abstract

It has been suggested that new massive gravity with higher order terms in the curvature may be renormalizable and thus a candidate for renormalizable quantum gravity. We show that three-dimensional gravity that contains quadratic scalar curvature and Ricci tensor is renormalizable, but those theories with special relation between their coefficients including new massive gravity are not.