CDT we refer the interested reader to [@cdtreviews; @physrep; @cdtlectures].

The central object of interest in the CDT approach to quantum gravity is the gravitational path integral, which in the continuum can be written formally as $$\label{eq:pigrav}
Z(G,\Lambda)=\hspace{-.6cm}\mathop{\int}_{\mathrm{geometries\, [g]}}\hspace{-.7cm}{\mathcal{D}[g]}\exp(iS_{\mathrm{EH}}[g]),$$ where $S_{\mathrm{EH}}[g]$ is the Einstein-Hilbert action, written as functional of the metric $g$, $\mathcal{D}[g]$ is a measure on the space of geometries (the space of equivalence classes $[g]$ of metrics under the action of the diffeomorphism group), $G$ is Newton’s constant and $\Lambda$ is the cosmological constant. To define the path integral properly it needs to be regularized, which in CDT is done by performing the “sum over histories" (\[eq:pigrav\]) over a set of piecewise flat, simplicial Lorentzian geometries – in other words, triangulations – effectively discretizing the curvature degrees of freedom of spacetime. The way in which triangulations encode curvature is illustrated best in two dimensions. In the Euclidean plane, consider a flat disc consisting of six equilateral triangles which share a central vertex, and remove one of the triangles (Fig. \[fig:reggecurvature\], left). By identifying the opposite sides of the gap thus created, the piecewise flat disc acquires nontrivial (positive Gaussian) curvature, whose magnitude is equal to the deficit angle 