How to understand the Structure of Beta Functions in Six-derivative Quantum Gravity?

TL;DR

This paper analyzes the mathematical structure of beta functions in six-derivative quantum gravity, highlighting the role of coupling ratios and their relation to conformal symmetry and renormalizability.

Contribution

It provides a detailed examination of the exact beta functions in six-derivative quantum gravity and explores their dependence on coupling ratios and symmetry properties.

Findings

Beta functions depend polynomially on the ratio of couplings.

Enhanced conformal symmetry relates to the limit where the coupling ratio tends to infinity.

Six-derivative theories exhibit different renormalizability features compared to four-derivative models.

Abstract

We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in $d=4$ spacetime dimensions. The fundamental role here is played by the ratio $x$ of the coupling in front of the term with Weyl tensors to the coupling in front of the term with Ricci scalars in the original action. We draw a relation between the polynomial dependence on $x$ and the absence/presence of enhanced conformal symmetry and renormalizability in the models where formally $x\to+\infty$ in the case of four- and six-derivative theories respectively.