Gravity and Matter with Asymptotic Safety

TL;DR

This paper reviews the progress in asymptotic safety approaches to quantum gravity, emphasizing the role of fixed points and the impact of matter fields on the theory's consistency.

Contribution

It summarizes recent results on asymptotic safety in quantum gravity and analyzes how matter fields influence the existence of fixed points.

Findings

Existence of a non-trivial fixed point is crucial for asymptotic safety.

Matter content constraints are necessary to maintain the fixed point.

Introduction of matter fields affects the renormalization group flow.

Abstract

Building a consistent Quantum Theory of Gravity is one of the most challenging aspects of modern theoretical physics. In the past couple of years, new attempts have been made along the path of ``asymptotic safety'' through the use of Exact Renormalisation Group Equations, which hinge on the existence of a non-trivial fixed point of the flow equations. We will first summarize the major results that have been obtained along these lines, then we will consider the effect of introducing matter fields into the theory. Our analyses show that in order to preserve the existence of the fixed point one must satisfy some constraints on the matter content of the theory.