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We perform a detailed investigation of the phase structure and thesemiclassical effective action of (2+1)-dimensional Causal DynamicalTriangulations (CDT) quantum gravity using computer simulations. On the onehand, we study the effect of enlarging the ensemble of triangulations byrelaxing the simplicial manifold conditions in a controlled way. On the otherhand, we cast a first look at CDT geometries with spatial topology beyond thatof the sphere or torus. We measure the phase structure of the model for severaltriangulation ensembles and spatial topologies, finding evidence that the phasestructure is qualitatively unaffected by these generalizations. Furthermore, wedetermine the effective action for the spatial volumes of the system, againvarying the simplicial manifold conditions and the spatial topology. In allcases where we were able to gather sufficient statistics, we found theresulting effective action to be consistent with a minisuperspace actionderived from continuum Einstein gravity. We interpret our overall results asevidence that 1) partially relaxing simplicial manifold conditions or changingthe spatial genus does not affect the continuum limit of 3D CDT and that 2)increasing the spatial genus of the system likely does not influence theleading-order terms in the emergent effective action.

The phase structure and effective action of 3D CDT at higher spatial genus