Evidence for Asymptotic Safety from Lattice Quantum Gravity

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of $\sim 3/2$ at short distance to $\sim 4$ 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.

Figure 1

Schematic of the phase diagram as a function of ${\kappa }_2$ and $\beta$.

Figure 2

Spectral dimension as a function of diffusion time $\sigma$, including a fit to Eq. (7). The width of the band shows the statistical error in the fit.