Quantum Gravity and Effective Topology

          @misc{ pirsa_PIRSA:25050037,
            doi = {10.48660/25050037},
            url = {https://pirsa.org/25050037},
            author = {Loll, Renate},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Quantum Gravity and Effective Topology},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {may},
            note = {PIRSA:25050037 see, \url{https://pirsa.org}}
          }
          

Abstract

My presentation will 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 homology of a sequence of coarse-grained versions of the geometry as a function of the coarse-graining scale. This gives rise to a characteristic "topological finger print" of the quantum geometry. I discuss the results for Lorentzian and Euclidean 2D quantum gravity, defined via lattice quantum gravity based on causal and Euclidean DT. For the latter, our numerical analysis reproduces the well-known string susceptibility exponent governing the scaling behaviour of the partition function.   [Joint work with Jesse van der Duin, Marc Schiffer and Agustin Silva, to appear.]