Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields Original Research Article

We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to d massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a image “barrier”, analogous to the image barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For image we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For image the effective average geometry is no longer toroidal but “semiclassical” and spherical with Hausdorff dimension image. In the image sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described by an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Hořava–Lifshitz models.