Flatness, Non-flatness, and Orientations in Ponzano-Regge

          @misc{ pirsa_PIRSA:25060086,
            doi = {10.48660/25060086},
            url = {https://pirsa.org/25060086},
            author = {Engle, Jonathan},
            keywords = {},
            language = {en},
            title = {Flatness, Non-flatness, and Orientations in Ponzano-Regge},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {jun},
            note = {PIRSA:25060086 see, \url{https://pirsa.org}}
          }
          

Abstract

The original spinfoam model, the Ponzano-Regge spinfoam model of 3D Euclidean gravity with zero cosmological constant, has two properties in seeming contradiction: (1.) Its connection formulation consists in the imposition of exact flatness, and (2.) Its sum-over-spins formulation has, as its leading order large spin asymptotics, Regge calculus, modified to include an additional local discrete orientation variable for each tetrahedron, which, when fixed inhomogeneously, leads to critical point equations for the edge lengths which do not imply flatness, but rather allow spikes. We explore possible resolutions to this paradox which may also have relevance for the semiclassical regime of both Euclidean and Lorentzian 4D spinfoams, with both zero and non-zero cosmological constant, in which a similar sum over local orientations appears.