Spectral Observables and Gauge Field Couplings in Causal Dynamical Triangulations

In the first part of this Chapter, we discuss the role of spectral observables, describing possible ways to build them from discretizations of the Laplace-Beltrami operator on triangulations, and how to extract useful geometric information. In the second part, we discuss how to simulate the composite system of gauge fields coupled to CDT for generic groups and dimensions, showing results in some specific case and pointing out current challenges.