Nonperturbative Quantum Gravity

TL;DR

This paper discusses nonperturbative approaches to quantum gravity, focusing on asymptotic safety and Causal Dynamical Triangulations (CDT), exploring their formalism, phase structure, and potential to identify ultraviolet fixed points.

Contribution

It provides a comprehensive overview of CDT formalism, phase diagram, fixed points, and its potential to support asymptotic safety in quantum gravity.

Findings

Evidence for possible UV fixed points in CDT

Emergence of quantum geometries in different phases

Potential connection between CDT and Hořava-Lifshitz gravity

Abstract

Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum. "Causal Dynamical Triangulations" (CDT) is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a UV fixed point. We describe the formalism of CDT, its phase diagram, possible fixed points and the "quantum geometries" which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Ho\v{r}ava-Lifshitz gravitational models.