Quantum Gravity and Effective Topology

Abstract

We introduce a new methodology to characterize properties of quantum spacetime in a strongly quantum-fluctuating regime, using tools from topological data analysis. Starting from a microscopic quantum geometry, generated nonperturbatively in terms of dynamical triangulations (DT), we compute the Betti numbers of a sequence of coarse-grained versions of the geometry as a function of the coarse-graining scale, yielding a characteristic ``topological finger print". We successfully implement this methodology in Lorentzian and Euclidean 2D quantum gravity, defined via lattice quantum gravity based on causal and Euclidean DT, yielding different results. Effective topology also enables us to formulate necessary conditions for the recovery of spacetime symmetries in a classical limit.