Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms

TL;DR

This paper investigates the decoupling of massive ghost modes in a 4D conformal factor model, analyzing one-loop nonlocal form factors to understand UV and IR behaviors and implications for the cosmological constant.

Contribution

It provides a detailed analysis of quantum decoupling in the Antoniadis-Mottola model, connecting UV behavior with IR irrelevance of ghost modes and exploring cosmological implications.

Findings

UV beta functions match previous results

IR ghost contributions become irrelevant

Light mode dynamics dominate low-energy behavior

Abstract

We explore the decoupling of massive ghost mode in the $4D$ (four-dimensional) theory of the conformal factor of the metric. The model was introduced by Antoniadis and Mottola in [1] and can be regarded as a close analog of the fourth-derivative quantum gravity. The analysis of the derived one-loop nonlocal form factors includes their asymptotic behavior in the UV and IR limits. In the UV (high energy) domain, our results reproduce the Minimal Subtraction scheme-based beta functions of [1]. In the IR (i.e., at low energies), the diagrams with massive ghost internal lines collapse into tadpole-type graphs without nonlocal contributions and become irrelevant. On the other hand, those structures that contribute to the running of parameters of the action and survive in the IR, are well-correlated with the divergent part (or the leading in UV contributions to the form factors), coming from the effective low-energy theory of the conformal factor. This effective theory describes only the light propagating mode. Finally, we discuss whether these results may shed light on the possible running of the cosmological constant at low energies.