Quantum Gravity via Causal Dynamical Triangulations

TL;DR

Causal Dynamical Triangulations (CDT) offers a non-perturbative lattice approach to quantum gravity, exploring phase structures and quantum geometries, with potential links to asymptotic safety and Horava-Lifshitz models.

Contribution

This paper formalizes CDT, analyzes its phase diagram, and discusses its capability to model various quantum gravitational theories beyond traditional frameworks.

Findings

Identification of the phase diagram of CDT

Emergence of quantum geometries from the formalism

Potential connection to asymptotic safety and Horava-Lifshitz models

Abstract

"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be used to define a continuum quantum field theory, potentially making contact with quantum gravity defined via asymptotic safety. We describe the formalism of CDT, its phase diagram, and the quantum geometries emerging from it. We also argue that the formalism should be able to describe a more general class of quantum-gravitational models of Horava-Lifshitz type.