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

Understand

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 $c=1$ "barrier", analogous to the $c=1$ barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically.
• For $d\leq 1$ we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand.
• For $d>1$ the effective average geometry is no longer toroidal but "semiclassical" and spherical with Hausdorff dimension $d_H = 3$.