Z = ∑T e−S_Regge[T] | Ambjørn–Jurkiewicz–Loll 1998
Simplices: —S_Regge = —d_H ≈ —Moves: 0
Causal Dynamical Triangulations (CDT) is a background-independent approach to quantum gravity
(Ambjørn, Jurkiewicz, Loll) that path-integrates over Lorentzian geometries with a causal structure.
Spacetime is approximated by a triangulation with fixed time-slicing, and the partition function
Z = ∑_T e^{-S_Regge[T]} sums over all triangulations with the Regge action.
The crucial CDT insight is that restricting to causal triangulations (no spatial topology change)
automatically generates a 4D de Sitter-like semiclassical spacetime — unlike Euclidean DT which produces
branched polymers or crumpled phases. The visualization shows the 1+1D CDT as a random triangulated cylinder
with Markov-chain Monte Carlo moves (Alexander/Pachner moves: (2,2) flip, (1,3) and (3,1) bubble).
The Hausdorff dimension d_H and spectral dimension d_s are measured from the random walk return probability.