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arXiv · 1201.1590

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

J. Ambjorn·A. T. Goerlich·J. Jurkiewicz·H. -G. Zhang
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Abstract

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 $d_H = 3$. In the $d>1$ sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described 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.

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J. Ambjorn, A. T. Goerlich, J. Jurkiewicz, H. -G. Zhang. 2012-01-07. Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields. https://doi.org/10.1016/j.nuclphysb.2012.05.024

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