Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions

TL;DR

This paper derives one-loop beta functions for higher derivative gravity in various dimensions, demonstrating the existence of nontrivial UV fixed points and asymptotic safety, with special attention to four dimensions and Weyl invariance.

Contribution

It provides a comprehensive analysis of higher derivative gravity's renormalization group flow across multiple dimensions, revealing fixed points and asymptotic safety.

Findings

Nontrivial UV fixed points found in all studied dimensions.

Asymptotic safety established for higher derivative gravity in these dimensions.

Weyl-invariant fixed point possibly exists in four 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.