title: Critical gravity in four dimensions.
abstract: We study four-dimensional gravity theories that are rendered renormalizable by the inclusion of curvature-squared terms to the usual Einstein action with a cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "new massive gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild-type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.
authors.affiliation: China Economics and Management Academy, Central University of Finance and Economics, Beijing, China.
authors.forename: H
authors.initials: H
authors.lastname: Lü
authors.forename: C N
authors.initials: CN
authors.lastname: Pope