Conformal Symmetry in Field Theory and in Quantum Gravity

TL;DR

This paper develops a UV-finite, ghost-free quantum conformal gravity theory that maintains conformal invariance and explores its implications for scattering amplitudes, effective action, and unitarity, advancing understanding of quantum gravity.

Contribution

It introduces a UV-finite, non-local quantum conformal gravity model with preserved unitarity and vanishing conformal anomaly, utilizing the dilaton trick for manifest invariance.

Findings

The theory is UV-finite and ghost-free.

Conformal anomaly can be eliminated by fine-tuning.

Constraints on effective action and scattering amplitudes are derived.

Abstract

Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities are solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory is safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly vanishes by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented.