# Renormalizability in $D$-dimensional higher-order gravity

## TL;DR

This paper derives a simple method to compute the classical potential in D-dimensional higher-order gravity models and investigates the link between potential regularity at the origin and renormalizability.

## Contribution

It introduces a new expression for the classical potential and examines its relation to the renormalizability of higher-order gravity models, clarifying a long-standing conjecture.

## Key findings

- Renormalizable higher-order gravity models tend to have nonsingular classical potentials at the origin.
- The converse is not necessarily true; nonsingular potential does not imply renormalizability.
- Analysis confirms the conjecture for specific fourth- and sixth-order gravity models.

## Abstract

A simple expression for calculating the classical potential concerning $D$-dimensional gravitational models is obtained through a method based on the generating functional. The prescription is then used as a mathematical tool to probe the conjecture that renormalizable higher-order gravity models --- which are, of course, nonunitary --- are endowed with a classical potential that is nonsingular at the origin. It is also shown that the converse of this statement is not true, which implies that the finiteness of the classical potential at the origin is a necessary but not a sufficient condition for the renormalizability of the model. The systems we have utilized to verify the conjecture were fourth- and sixth- order gravity models in $D$-dimensions. A discussion about the polemic question related to the renormalizability of new massive gravity, which Oda claimed to be renormalizable in 2009 and three years late was shown to be nonrenormalizable by Muneyuki and Ohta, is considered. We remark that the solution of this issue is straightforward if the aforementioned conjecture is employed. We point out that our analysis is restricted to local models in which the propagator has simple and real poles.