Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions

Abstract

We derive the one-loop beta functions for a theory of gravity with generic action containing up to four derivatives. The calculation is done in arbitrary dimension and on an arbitrary background. The special cases of three, four, near four, five and six dimensions are discussed in some detail. We find that the theories have nontrivial UV fixed points and are asymptotically safe in all dimensions we study. We also find an indication that Weyl-invariant fixed point exists in four dimensions. The new massive gravity in three dimensions does not correspond to any fixed point.

32 pages, 5 figures, v2: slightly modified and typos corrected. Version to be published in Class. Quant. Grav