Evidence for Asymptotic Safety from Lattice Quantum Gravity

Abstract

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ∼3/2 at short distance to ∼4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.

Asymptotic Safety, Fractals, and Cosmology

“…Furthermore, the authors of ref. [67] reported simulations within the euclidean dynamical triangulation (EDT) approach in d = 4, which favor a drop of the spectral dimension from 4 to about 1.5; this is again in conflict with the QEG expectations if one interprets the latter dimension as the value in the continuum limit.…”

“…In particular, it is easily accessible in Monte Carlo simulations of the Causal Dynamical Triangulations (CDT) approach in d = 4 [61] and d = 3 [63] as well as in Euclidean Dynamical Triangulations (EDT) [67]. This feature allows a direct comparison between D CDT s (T ) and D EDT s (T ) obtained within the discrete approaches and D QEG s (T ) capturing the fractal properties of the QEG effective space-times.…”

“…This mismatch decreases systematically for larger triangulations Fig. 5 with the fitting functions used in the CDT [61] or EDT [67] simulations shows that all the Monte Carlo data points obtained are positioned on the infrared side of the turning point of the RG trajectories underlying the QEG effective space-times. They neither probe the semi-classical plateau nor the scaling regime of the NGFP.…”

Quantum Gravity via Causal Dynamical Triangulations

“…Even if this is the case, it is in principle possible that by adding more terms to the bare lattice action and suitably tuning the associated new coupling constants, an interesting continuum theory may emerge after all. This possibility has been investigated in the past [19], as well as more recently [20], but there is no conclusive evidence at this point that these modified Euclidean models can reproduce the physical properties of quantum gravity from CDT, the Lorentzian lattice gravity theory to which we will turn next (see also [21] for a variety of reviews of the subject). Fig.…”

“…In (20), N 0 (T ) denotes the number of vertices in the triangulation T , and N 4 (T ) the number of its foursimplices. The coupling κ 0 is related to the gravitational coupling constant G via 1/κ 0 ∝ Ga 2 , and κ 4 should be identified with a 4 Λ/G, where Λ is the cosmological constant.…”