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

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 $d\le 1$ 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.

19 pages, many figures

References in corpus (12)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• The Nonperturbative Quantum de Sitter Universe
• A second-order phase transition in CDT
• Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
• A String Field Theory based on Causal Dynamical Triangulations
• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• A new continuum limit of matrix models
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Putting a cap on causality violations in CDT
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• 3D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model

Cited by in corpus (14)

• Quantum Gravity from Causal Dynamical Triangulations: A Review
• New multicritical matrix models and multicritical 2d CDT
• Locally Causal Dynamical Triangulations in Two Dimensions
• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• 2d CDT with gauge fields
• The microscopic structure of 2D CDT coupled to matter
• Scalar fields in Causal Dynamical Triangulations
• A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?
• A restricted dimer model on a 2-dimensional random causal triangulation
• Is Lattice Quantum Gravity Asymptotically Safe? Making contact between Causal Dynamical Triangulations and the Functional Renormalization Group
• The spectral dimension in 2D CDT gravity coupled to scalar fields
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Towards elucidation of zero-temperature criticality of Ising model on 2d DT
• Analytical approaches to 2D CDT coupled to matter