Is lattice quantum gravity asymptotically safe? Making contact between causal dynamical triangulations and the functional renormalization group

We compare the effective action of the scale factor obtained from lattice quantum gravity [in the form of causal dynamical triangulations (CDT)] to the corresponding effective action obtained from the simplest functional renormalization group (FRG) calculation. In this way, we can identify the generic infinite four-volume limit of the lattice theory in the so-called de Sitter phase with the Gaussian fixed-point limit or the IR fixed-point limit obtained by FRG. We also show how to identify a putative UV lattice gravity fixed point. Our Monte Carlo simulations of CDT allow for the existence of such a UV fixed point, although the data precision does not yet provide a proof of its existence. The concept of a correlation length relevant for the lattice gravity fixed points is argued to be different from the concept of correlation lengths encountered in field theories in a fixed spacetime background. Published by the American Physical Society 2024