Infrared fixed point in quantum Einstein gravity

TL;DR

This paper investigates the infrared behavior of quantum Einstein gravity, revealing an attractive fixed point and analyzing the critical exponents, with implications for models exhibiting phase transitions.

Contribution

It provides a renormalization group analysis of quantum Einstein gravity in the infrared, identifying fixed points and their effects on correlation lengths.

Findings

Existence of an attractive infrared fixed point in the broken symmetric phase.

The IR critical exponent $ u$ is 1/2 due to the Gaussian fixed point.

Certain model extensions yield finite correlation lengths in the broken phase.

Abstract

We performed the renormalization group analysis of the quantum Einstein gravity in the deep infrared regime for different types of extensions of the model. It is shown that an attractive infrared point exists in the broken symmetric phase of the model. It is also shown that due to the Gaussian fixed point the IR critical exponent $\nu$ of the correlation length is 1/2. However, there exists a certain extension of the model which gives finite correlation length in the broken symmetric phase. It typically appears in case of models possessing a first order phase transitions as is demonstrated on the example of the scalar field theory with a Coleman-Weinberg potential.