Exploring a formulation of lattice quantum gravity

We report on a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations(EDT) with a non-trivial measure term in the path integral. We search the parameter space of EDT for a second-order critical point, whose divergent correlation length would at least in principle allow one to define a continuum limit, whereas the vanishing correlation length of a first-order critical point makes it unsuitable for this purpose. We also search the parameter space of EDT for a physical phase with 4-dimensional semiclassical geometry. We find that the parameter space contains three phases which we call the branched polymer phase, the collapsed phase, and the crinkled phase. We determine the order of the phase transition dividing the branched polymer phase from the collapsed phase to be first-order. The transition dividing the collapsed phase from the crinkled phase appears to be an analytic cross-over, or a third or higher-order transition. The effective dimension of each phase in the parameter space is studied. We report that EDT with a nontrivial measure term does not appear to contain a phase with 4-dimensional semiclassical geometry. We argue that within a physical 4-dimensional semiclassical phase, such as that found in causal dynamical triangulations (CDT), a dynamical dimensional reduction from 4 on macroscopic scales to 3/2 on microscopic scales may resolve the tension between asymptotic safety and the holographic principle