# Renormalization group in super-renormalizable quantum gravity

## TL;DR

This paper calculates the exact one-loop beta function for the Newton constant in super-renormalizable quantum gravity models, demonstrating gauge independence and discussing implications for nonlocal theories free of ghost states.

## Contribution

It provides a gauge-independent one-loop beta function calculation for the Newton constant in super-renormalizable quantum gravity models using Barvinsky-Vilkovisky technology.

## Key findings

- Beta function is well-defined and gauge-independent.
- Applicable to a broad class of nonlocal gravitational theories.
- Supports the consistency of nonlocal models without ghost states.

## Abstract

One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky-Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive ghost-like states at the tree-level.