One loop renormalization of the four-dimensional theory for quantum dilaton gravity.

TL;DR

This paper investigates the one-loop renormalization of a general four-dimensional metric-dilaton gravity theory, showing how certain divergences can be absorbed, leading to a running cosmological constant and potential implications for low-energy physics.

Contribution

It provides the first detailed calculation of one-loop divergences in the most general metric-dilaton theory with second derivative terms, revealing how to fine-tune functions to eliminate higher derivative counterterms.

Findings

Higher derivative counterterms can be eliminated on shell by tuning functions.

The dilaton field acquires an anomalous dimension, causing the cosmological constant to run.

Some solutions yield a small observable cosmological constant at low energies.

Abstract

We study the one loop renormalization in the most general metric-dilaton theory with the second derivative terms only. The general theory can be divided into two classes, models of one are equivalent to conformally coupled with gravity scalar field and also to general relativity with cosmological term. The models of second class have one extra degree of freedom which corresponds to dilaton. We calculate the one loop divergences for the models of second class and find that the arbitrary functions of dilaton in the starting action can be fine-tuned in such a manner that all the higher derivative counterterms disappear on shell. The only structures in both classical action and counterterms, which survive on shell, are the potential (cosmological) ones. They can be removed by renormalization of the dilaton field which acquire the nontrivial anomalous dimension, that leads to the effective running of the cosmological constant. For some of the renormalizable solutions of the theory the observable low energy value of the cosmological constant is small as compared with the Newtonian constant. We also discuss another application of our result.