Quantum gravity from causal dynamical triangulations: a review

Abstract

This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory's phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications. 1 arXiv:1905.08669v1 [hep-th]

Predictive power of grand unification from quantum gravity

“…While the functional Renormalization Group (FRG) is the most commonly used tool to explore asymptotically safe gravity, it is by no means the only one. Lattice techniques [63], also with matter [64,65] and perturbative tools [66,67] are also employed.…”

Critical Reflections on Asymptotically Safe Gravity

“…There are two main ways in which discrete random geometries are explored: One can hold a triangulation fixed and vary the edge lengths, as in Regge calculus, or hold the edge lengths fixed but vary the triangulation, as in dynamical triangulations. The latter have developed in two research branches: Euclidean Dynamical Triangulations [220], and Causal Dynamical Triangulations [221,222].…”

“…In the case of Causal Dynamical Triangulations (CDT), the configuration space includes only configurations that admit a Wick rotation, see [222] for a review. Therefore, an analytical continuation to a Lorentzian path integral is in principle possible.…”

“…Moreover, Liouville gravity can be recovered by allowing for topology change of the spatial slices [227]. It has been stressed in [222] though that the equivalence of CDT and Horava-Lifshitz gravity may not extend beyond the two-dimensional case.…”

Quantum-Only Metrics in Spherically Symmetric Gravity

“…Efforts towards the unification of General Relativity and Quantum Mechanics into a coherent theory of Quantum Gravity were started long ago and have been intensifying in the last decades. In spite of big progress in loop Quantum Gravity [1,2], asymptotic safety [3] and discrete spacetime models [4][5][6][7], "the revolution is still unfinished", in the words of C. Rovelli. The spin-offs of this research work, however, are manifold and remarkable in their own right.…”