Renormalization group study of the higher derivative conformal scalar model

TL;DR

This paper investigates a higher derivative conformal scalar model, demonstrating its one-loop renormalizability and asymptotic freedom in the IR, contributing to understanding conformal invariance in quantum gravity theories.

Contribution

It introduces a new conformal scalar model with higher derivatives, showing its renormalizability and universal renormalization constants at one loop.

Findings

The model is renormalizable at one loop.

Renormalization constants are universal for any parametrization.

The theory exhibits asymptotic freedom in the IR limit.

Abstract

The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide the conformal invariance of the classical action. We find the corresponding quantum theory to be renormalizable at one loop, and the renormalization constants for the dimensionless parameters are explicitly shown to be universal for an arbitrary parametrization of the quantum field. The renormalization group equations indicate an asymptotic freedom in the IR limit. In this respect the theory is similar to the well-known model based on the anomaly-induced effective action.