On a renormalization group scheme for causal dynamical triangulations

Abstract

The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group schemein concert with finite size scaling analysis-is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in the first paper of this two-part series. As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.

Quantum gravity from causal dynamical triangulations: a review

“…Note that[85] interprets the measurements in the more general framework of Hořava-Lifshitz gravity, allowing also for a "deformed" de Sitter universe 24. Ref [87]. suggests the use of additional, alternative yardsticks, which one would like to extract from the behaviour of the spectral dimension, see Sec.…”

Setting the physical scale of dimensional reduction in causal dynamical triangulations

“…We approximate the expectation value E[D s (σ)] of D (Tc) s (σ) by the ensemble average D s (σ) . We follow the methods of [16] in estimating D s (σ) and its error.…”

“…G is the renormalized Newton constant, equivalent (for D = 3) to P / , and Λ is the renormalized cosmological constant. To make direct contact with our measurements of N SL 2 (τ ), we express the action (16) in terms of the spatial 2-volume V 2 (as opposed to the scale factor) as a function of the global time coordinate t.…”

“…Cooperman first advocated that measurements of D s (σ) could form the basis for a renormalization group analysis of causal dynamical triangulations, and he proposed a method for performing such an analysis [16]. Subsequently, Ambjørn et al attempted to track relative changes in the lattice spacing across the de Sitter phase with measurements of D s (σ) [1].…”

Scaling analyses of the spectral dimension in 3-dimensional causal dynamical triangulations

“…On the basis of these findings, I advance a tentative physical explanation for the dynamical reduction of the spectral dimension observed within causal dynamical triangulations: branched polymeric quantum geometry on sufficiently small scales. My analyses should facilitate attempts to employ the spectral dimension as a physical observable with which to delineate renormalization group trajectories in the hope of taking a continuum limit of causal dynamical triangulations at a nontrivial ultraviolet fixed point [3,6,21,22,26]. arXiv:1711.02685v1 [gr-qc] 7 Nov 2017 bare coupling k 0 of the Euclidean Regge action for causal triangulations.…”