Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories

TL;DR

This paper compares conditions for ultraviolet finiteness and asymptotic safety in quantum gravity, demonstrating a six-derivative model that achieves UV-finiteness without extra matter or symmetry, highlighting their compatibility.

Contribution

It shows that a six-derivative quantum gravitational theory can be UV-finite without matter or symmetry by adding cubic curvature terms, and discusses the relationship between finiteness and asymptotic safety.

Findings

A six-derivative gravity model can be UV-finite without matter.

UV-finiteness and asymptotic safety are compatible approaches.

UV-finite models are essential for defining the ultraviolet limit at fixed points.

Abstract

We present and discuss well known conditions for ultraviolet finiteness and asymptotic safety. The requirements for complete absence of ultraviolet divergences in quantum field theories and existence of a non-trivial fixed point for renormalization group flow in the ultraviolet regime are compared based on the example of a six-derivative quantum gravitational theory in $d=4$ spacetime dimensions. In this model, it is possible for the first time to have fully UV-finite quantum theory without adding matter or special symmetry, but by inclusion of additional terms cubic in curvatures. We comment on similarities and some apparent differences between the two approaches, but we show that they are both compatible to each other. Finally, we motivate the claim that actually asymptotic safety needs UV-finite models for providing explicit form of the ultraviolet limit of Wilsonian effective actions describing special situations at fixed points.