Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations

We study the behavior of holonomy spin foam partition functions, a form of lattice gauge gravity, on generic 4d-triangulations using micro local analysis. To do so we adapt tools from the renormalization theory of quantum field theory on curved space times. This allows us, for the first time, to study the partition function without taking any limits on the interior of the triangulation. We establish that for many of the most widely used models the geometricity constraints, which reduce the gauge theory to a geometric one, introduce strong accidental curvature constraints. These limit the curvature around each triangle of the triangulation to a finite set of values. We demonstrate how to modify the partition function to avoid this problem. Finally the new methods introduced provide a starting point for studying the regularization ambiguities and renormalization of the partition function.