A 3BF model of quantum gravity coupled to Standard Model matter

We develop an explicit model of quantum gravity coupled to the matter fields of the Standard Model, based on the 3-group structure and the 3BF action, within the framework of higher gauge theory. The model is constructed by providing a rigorous definition for the path integral of the theory, achieved by defining the whole theory on a piecewise-flat spacetime manifold. To that end, we develop a method to systematically discretize both the action and the path integral measure by passing from a smooth manifold to a piecewise-flat manifold. Finally, we discuss in some detail the structure of the resulting quantum gravity model, and provide a preliminary analysis of its semiclassical limit.