Running scales in causal dynamical triangulations

The search for typical length scales, eventually diverging at a critical point, is a major goal for lattice approaches looking for a continuum theory of quantum gravity. Within the simplicial Monte Carlo approach known as causal dynamical triangulations, we study the spectrum of the Laplace operator to infer the geometrical properties of triangulations. In some phase of the theory a discrete set of length scales emerges, persisting in the infinite volume limit; such scales run as a function of the bare couplings, consistently with a critical behavior around a possible second order transition.