On the Lorentz symmetry in conformally reduced Quantum Gravity

TL;DR

This paper investigates the behavior of Lorentz symmetry in conformally reduced quantum gravity using the functional renormalization group, revealing symmetry breaking near the Reuter fixed point and identifying a new relevant curvature coupling.

Contribution

It extends the FRG analysis by separately evolving time and space derivatives, uncovering Lorentz symmetry breaking and a new relevant curvature coupling in quantum gravity.

Findings

Reuter fixed point identified in the ultraviolet region.

Lorentz symmetry breaks down near the Reuter fixed point.

A new relevant curvature coupling is discovered.

Abstract

The functional renormalization group treatment of the conform reduced Einstein-Hilbert gravity is extended by following the evolution of the time and space derivatives separately, in order to consider the Lorentz symmetry during the evolution. We found the Reuter fixed point in the ultraviolet region. It is shown that starting from the Gaussian fixed point the Lorentz symmetry breaks down in the vicinity of the Reuter fixed point. Similarly, in the symmetry broken phase it also breaks down in the infrared region close to a critical singularity scale. By calculating the anomalous dimension form the kinetic term of the action, we found a new relevant coupling belonging to the curvature.