Unitarity versus Renormalizability of Higher Derivative Gravity in 3D

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.

9 pages. v2: title changed, minor modification. v3: minor corrections to match the published version