# Causal Dynamical Triangulations

This webpage is dedicated to curating all the papers on Causal Dynamical Triangulations (CDT), Generalised CDT (GCDT), and Euclidean Dynamical Triangulations (EDT).

♦ EDT was invented by Jan Ambjørn, Jerzy Jurkiewicz, and many others $^\dagger$

♦ CDT was invented by Jan Ambjørn, Renata Loll, and Jerzy Jurkiewicz $^\dagger$

♦ GCDT was invented by Jan Ambjorn, Renata Loll, Willem Westra, and Stefan Zohren $^\dagger$

▞ EDT, CDT, and GCDT are the non-perturbative quantum gravity models. EDT is a precursor to CDT, and causality is the demarcation between them. EDT was started in the 1980s in the context of non-critical bosonic string theory$^\dagger$, and it was initially known in the scientific community as Dynamical Triangulations (DT). It is based on Regge’s coordinate-free approach$^\dagger$ where the continuous manifolds are replaced by piecewise flat simplicial manifolds, with all edge-length fixed to a lattice cut-off such that summing over all possible simplicial manifolds results in background independence. To show the distinctness between CDT, we say EDT instead of DT. But, both names mean the same. CDT is a precursor to GCDT, and relaxation of preferred foliation is the distinction between them. CDT was initially called Lorentzian quantum gravity.

▛ *Note that CDT, GCDT, and EDT do not assume that the discreteness they impose is fundamental or physical. Rather it is an approximation technique. But for example, Causal Set Theory and other discrete approaches of quantum gravity assume that it’s physical.*

▛

**See the Influence Map based on based on the 1998 Ambjorn and Loll paper:**

▟

**Read the most recent papers on CDT in arXiv.**

Open Knowledge Map for CDT Research :)

**Contributors**

Jan Ambjørn, Jerzy Jurkiewicz, Renata Loll, Andrzej Görlich, Jakub Gizbert-Studnicki, Dániel Németh, Marcus Reitz, __Damodar Rajbhandari__, Timothy Budd, Yoshiyuki Watabiki, Zbigniew Drogosz, Nilas Klitgaard, Stefan Zohren, Willem Westra, Hiroyuki Fuji, Samo Jordan, Lisa Glaser, Yuki Sato, Hongguang Zhang, Jack Laiho, Ben Ruijl, Konstantinos N. Anagnostopoulos, Charlotte Floe Kristjansen, Dario Benedetti, Joe Henson, Joshua H. Cooperman, Rajesh Kommu, Steven Carlip, Jonah Miller, Christian Anderson, Patrick R. Zulkowski, Piotr Bialas, Thordur Jonsson, John F. Wheater, Ray Renken, Simon Catterall, Simeon Warner, John B. Kogut, Bergfinnur Durhuus, Annalisa Marzuoli, Mauro Carfora, Bertrand Eynard, Alicia Castro, … yet to be updated.

**Note:** *Contributors are those who published EDT/CDT/GCDT articles in peer-reviewed journals. The order does not signify the higher contributions.*

▞ This webpage will keep on updating as I find more papers on this topic. I will also try to keep the list in the suitable group in chronological order (newest first).**Note:** *The year I will mention before the title is the year the paper was uploaded to arXiv (except theses), and the link will be to the arXiv most recent version of the paper.*

▛ *Find articles using Ctrl+F on PC, or Command+F on Mac, and search with ?<search-id> where <search-id> can be 2D, 3D, 4D, EDT, CDT, and GCDT.*

▟

*Access this webpage using PhysicsLog.com/cdt.*

▞

*If you want to add your (EDT/CDT/GCDT) article or thesis or name as an (EDT/CDT/GCDT) contributor to this webpage, please contact me at*

`[firstname][AT]PhysicsLog.com`

.## Formalism

- 2023 - Spectral Observables and Gauge Field Couplings in Causal Dynamical Triangulations $\mid$ ?CDT $\mid$ Book Chapter
- 2023 - Quantum Curvature as Key to the Quantum Universe $\mid$ ?CDT $\mid$ Book Chapter
- 2023 - Semiclassical and Continuum Limits of Four-Dimensional CDT $\mid$ ?CDT $\mid$ Book Chapter
- 2022 - Landau Theory of Causal Dynamical Triangulations $\mid$ ?CDT $\mid$ Book Chapter
- 2022 - The causality road from dynamical triangulations to quantum gravity that describes our Universe $\mid$ ?EDT $\mid$ Book Chapter
- 2022 - Lattice Quantum Gravity: EDT and CDT $\mid$ ?EDT $\mid$ ?CDT $\mid$ Review
- 2022 - Lessons from the Mathematics of Two-Dimensional Euclidean Quantum Gravity $\mid$ ?2D $\mid$ ?EDT
- 2021 - CDT Quantum Toroidal Spacetimes: An Overview $\mid$ ?4D $\mid$ ?CDT $\mid$ Review
- 2020 - Renormalization in quantum theories of geometry $\mid$ ?4D $\mid$ ?CDT $\mid$ Review
- 2019 - Quantum gravity on a torus $\mid$ ?4D $\mid$ ?CDT $\mid$ Review
- 2019 - Quantum Gravity from Causal Dynamical Triangulations: A Review $\mid$ ?CDT $\mid$ Review of recent progress till 2019
- 2015 - Locally Causal Dynamical Triangulations in Two Dimensions $\mid$ ?2D $\mid$ ?CDT
- 2015 - Recent results in CDT quantum gravity $\mid$ ?CDT
- 2013 - Causal Dynamical Triangulations without Preferred Foliation $\mid$ ?3D $\mid$ ?GCDT $\mid$ Showed that CDT results are independent of the foliation.
- 2013 - Quantum Gravity via Causal Dynamical Triangulations $\mid$ ?4D $\mid$ ?CDT $\mid$ Book Chapter
- 2013 - The transfer matrix in four-dimensional Causal Dynamical Triangulations $\mid$ ?4D $\mid$ ?CDT $\mid$ Book Chapter
- 2012 - Quantum gravity on a laptop: 1 + 1 Dimensional Causal Dynamical Triangulation simulation $\mid$ ?2D $\mid$ ?CDT
- 2012 - Nonperturbative Quantum Gravity $\mid$ Review of the CDT model from the beginning till 2012 $\mid$ CDT handbook
- 2011 - A Validation of Causal Dynamical Triangulations $\mid$ ?CDT $\mid$ Independently verified the CDT results
- 2010 - CDT- an Entropic Theory of Quantum Gravity $\mid$ ?2D $\mid$ ?4D $\mid$ ?CDT $\mid$ Lecture Note
- 2010 - Causal Dynamical Triangulations and the Quest for Quantum Gravity $\mid$ ?4D $\mid$ ?CDT $\mid$ Book Chapter
- 2007 - Putting a cap on causality violations in CDT $\mid$ ?2D $\mid$ ?GCDT $\mid$ First paper on GCDT
- 2006 - Unexpected Spin-Off from Quantum Gravity $\mid$ ?2D $\mid$ ?CDT
- 2005 - The Universe from Scratch $\mid$ Review
- 2002 - Simplicial Euclidean and Lorentzian Quantum Gravity $\mid$ ?EDT $\mid$ ?CDT
- 2001 - Generalized Lorentzian Triangulations and the Calogero Hamiltonian $\mid$ ?2D $\mid$ ?CDT
- 2001 - Dynamically triangulating Lorentzian quantum gravity $\mid$ ?CDT $\mid$ Introduced the numerical method for 4D CDT.
- 2000 - A non-perturbative Lorentzian path integral for gravity $\mid$ ?CDT
- 2000 - Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results $\mid$ ?2D $\mid$ ?3D $\mid$ ?EDT $\mid$ ?CDT $\mid$ Review
- 1999 - Integrable 2D Lorentzian Gravity and Random Walks $\mid$ ?2D $\mid$ ?CDT $\mid$ Used also the squares along with triangles to build the 2D triangulation.
- 1998 - Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change $\mid$ ?2D $\mid$ ?CDT $\mid$ First paper on CDT $\mid$ Analytical solved the 2D CDT.
- 1998 - Discrete approaches to quantum gravity in four dimensions $\mid$ ?4D $\mid$ ?EDT $\mid$ Review
- 1995 - Dynamical Triangulations, a Gateway to Quantum Gravity ? $\mid$ ?2D $\mid$ ?EDT
- 1994 - Quantization of Geometry $\mid$ ?EDT $\mid$ Lecture Note
- 1993 - Simplicial Quantum Gravity and Random Lattices $\mid$ ?EDT $\mid$ Lecture Note
- 1991 - Three-Dimensional Simplicial Quantum Gravity and Generalized Matrix Models $\mid$ ?3D $\mid$ ?EDT $\mid$ Not in arXiv

## Renormalization Group Flow

- 2022 - The phase structure and effective action of 3D CDT at higher spatial genus $\mid$ ?3D $\mid$ ?CDT $\mid$ code
- 2022 - Topology induced first-order phase transitions in lattice quantum gravity $\mid$ ?CDT
- 2021 - Critical behaviour of loop models on causal triangulations $\mid$ ?2D $\mid$ ?CDT
- 2021 - The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations $\mid$ ?2D $\mid$ ?CDT
- 2020 - The higher-order phase transition in toroidal CDT $\mid$ ?4D $\mid$ ?CDT
- 2019 - Towards an UV fixed point in CDT gravity $\mid$ ?CDT
- 2019 - Critical Phenomena in Causal Dynamical Triangulations $\mid$ ?CDT
- 2018 - The phase structure of Causal Dynamical Triangulations with toroidal spatial topology $\mid$ ?CDT
- 2018 - Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation $\mid$ ?CDT
- 2017 - Phase structure of Causal Dynamical Triangulations in 4D $\mid$ ?4D $\mid$ ?CDT $\mid$ Review on the bifurcation phase.
- 2017 - New higher-order transition in causal dynamical triangulations $\mid$ ?CDT
- 2016 - Characteristics of the new phase in CDT $\mid$ ?CDT $\mid$ Explained clearly how to fine-tune $\kappa_4$ so that CDT spacetime fluctuates around the target volume during the thermalization. Once the spacetime is thermalized, the $\kappa_4$ is fixed.
- 2016 - Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model $\mid$ ?3D $\mid$ ?CDT
- 2016 - A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations $\mid$ ?3D $\mid$ ?CDT
- 2015 - Exploring the new phase transition of CDT $\mid$ ?4D $\mid$ ?CDT
- 2014 - A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations $\mid$ ?3D $\mid$ ?CDT
- 2014 - Renormalization of lattice-regularized quantum gravity models I. General considerations $\mid$ ?CDT
- 2014 - Renormalization of lattice-regularized quantum gravity models II. The case of causal dynamical triangulations $\mid$ ?CDT
- 2014 - Renormalization Group Flow in CDT $\mid$ ?CDT
- 2013 - Euclidian 4d quantum gravity with a non-trivial measure term $\mid$ ?4D $\mid$ ?EDT
- 2012 - Second and First Order Phase Transitions in CDT $\mid$ ?CDT
- 2012 - New multicritical matrix models and multicritical 2d CDT $\mid$ ?2D $\mid$ ?CDT
- 2011 - A second-order phase transition in CDT $\mid$ ?CDT
- 2009 - Coarse graining dynamical triangulations: a new scheme $\mid$ ?EDT $\mid$ ?CDT
- 2006 - Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations $\mid$ ?2D $\mid$ ?CDT
- 2000 - Non-perturbative 3d Lorentzian Quantum Gravity $\mid$ ?3D $\mid$ ?CDT $\mid$ Introduced the numerical method for 3D CDT.
- 1999 - Crossing the c=1 barrier in 2d Lorentzian quantum gravity $\mid$ ?2D $\mid$ ?CDT $\mid$ Provided evidence for the conjecture that the KPZ values of the critical exponents in 2d EDT are entirely due to the presence of baby universes.
- 1998 - Phase diagram of three-dimensional dynamical triangulations with a boundary $\mid$ ?3D $\mid$ ?EDT
- 1998 - Phase diagram of the mean field model of simplicial gravity $\mid$ ?EDT
- 1998 - Crumpled triangulations and critical points in 4D simplicial quantum gravity $\mid$ ?4D $\mid$ ?EDT
- 1997 - Phase Structure of Dynamical Triangulation Models in Three Dimensions $\mid$ ?3D $\mid$ ?EDT
- 1997 - Polymeric Phase of Simplicial Quantum Gravity $\mid$ ?4D $\mid$ ?EDT
- 1997 - Singular Structure in 4D Simplicial Gravity $\mid$ ?4D $\mid$ ?EDT
- 1996 - Appearence of Mother Universe and Singular Vertices in Random Geometries $\mid$ ?4D $\mid$ ?EDT
- 1996 - A Renormalization Group for Dynamical Triangulations in Arbitrary Dimensions $\mid$ ?3D $\mid$ ?4D $\mid$ ?EDT
- 1996 - The Renormalization Group and Dynamical Triangulations $\mid$ ?EDT
- 1996 - Simplicial Gravity in Dimension Greater than Two $\mid$ ?EDT
- 1996 - The geometry of dynamical triangulations $\mid$ ?3D $\mid$ ?4D $\mid$ ?EDT
- 1996 - Further evidence that the transition of 4D dynamical triangulation is 1st order $\mid$ ?4D $\mid$ ?EDT $\mid$ Independently confirmed the first-order transition of DT.
- 1996 - Focusing on the Fixed Point of 4D Simplicial Gravity $\mid$ ?4D $\mid$ ?EDT $\mid$ It has been discovered that DT phases are of first-order transition, and became languished in this direction.
- 1996 - RG flow in an exactly solvable model with fluctuating geometry $\mid$ ?2D $\mid$ ?EDT
- 1995 - A Real-Space Renormalization Group for Random Surfaces $\mid$ ?EDT
- 1994 - Random Geometries and Real Space Renormalization Group $\mid$ ?2D $\mid$ ?EDT
- 1994 - A Random Surface Theory with Non-Trivial $\gamma_{\text{string}}$ $\mid$ ?2D $\mid$ ?EDT
- 1994 - Entropy and the Approach to the Thermodynamic Limit in Three-Dimensional Simplicial Gravity $\mid$ ?3D $\mid$ ?EDT
- 1994 - Phase Structure of Four Dimensional Simplicial Quantum Gravity $\mid$ ?4D $\mid$ ?EDT
- 1994 - Non-Perturbative Renormalization Group Flows in Two-Dimensional Quantum Gravity $\mid$ ?2D $\mid$ ?EDT
- 1994 - The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity $\mid$ ?2D $\mid$ ?EDT
- 1993 - Critical Phenomena for Riemannian Manifolds: Simple Homotopy and Simplicial Quantum Gravity $\mid$ ?3D $\mid$ ?EDT
- 1992 - The Theory of Dynamical Random Surfaces with Extrinsic Curvature $\mid$ ?2D $\mid$ ?EDT
- 1992 - Critical properties of the dynamical random surface with extrinsic curvature $\mid$ ?2D $\mid$ ?EDT $\mid$ Not in arXiv
- 1992 - Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions $\mid$ ?4D $\mid$ ?EDT

## Semi-classical Gravity

- 2021 - The de Sitter Instanton from Euclidean Dynamical Triangulations $\mid$ ?4D $\mid$ ?EDT
- 2021 - Scalar fields in Causal Dynamical Triangulations $\mid$ ?4D $\mid$ ?CDT $\mid$ Used harmonic co-ordinates to (lattice-type) CDT.
- 2020 - How round is the quantum de Sitter universe?
- 2019 - Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations $\mid$ ?CDT
- 2019 - Minisuperspace results for causal dynamical triangulations $\mid$ ?CDT
- 2017 - Four-dimensional CDT with toroidal topology $\mid$ ?4D $\mid$ ?CDT
- 2016 - Impact of topology in causal dynamical triangulations quantum gravity $\mid$ ?CDT $\mid$ First paper in toroidal topology $T^{4} \equiv S^{1}\times S^{1}\times S^{1}\times S^{1}$ $\mid$ You can read the construction of initial triangulation with that topology. $\mid$ The construction was inspired from the work by P. S. Mara’s “1975 - Triangulations for the Cube”.
- 2015 - Signature Change of the Metric in CDT Quantum Gravity? $\mid$ ?CDT $\mid$ First paper to report the bifurcation phase in CDT
- 2014 - The effective action in 4-dim CDT. The transfer matrix approach $\mid$ ?4D $\mid$ ?CDT
- 2014 - A note on the Lee-Yang singularity coupled to 2d quantum gravity $\mid$ ?2D $\mid$ ?CDT
- 2013 - De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation $\mid$ ?3D $\mid$ ?GCDT
- 2012 - Quantum widening of CDT universe $\mid$ ?4D $\mid$ ?CDT
- 2012 - The transfer matrix in four-dimensional CDT $\mid$ ?4D $\mid$ ?CDT
- 2011 - The Semiclassical Limit of Causal Dynamical Triangulations $\mid$ ?CDT
- 2010 - Geometry of the quantum universe $\mid$ ?4D $\mid$ ?CDT
- 2009 - Can causal dynamical triangulations probe factor-ordering issues? $\mid$ ?CDT
- 2008 - The Nonperturbative Quantum de Sitter Universe
- 2007 - The Emergence of Spacetime, or, Quantum Gravity on Your Desktop $\mid$ ?4D $\mid$ ?CDT
- 2007 - Planckian Birth of the Quantum de Sitter Universe $\mid$ ?4D $\mid$ ?CDT $\mid$ Showed that the linear size of the quantum universes under study is in-between 17 and 28 Planck lengths.
- 2006 - Quantum Gravity, or The Art of Building Spacetime $\mid$ ?4D $\mid$ ?CDT $\mid$ Book Chapter
- 2005 - Reconstructing the Universe
- 2004 - Semiclassical Universe from First Principles $\mid$ ?4D $\mid$ ?CDT
- 2004 - Emergence of a 4D World from Causal Quantum Gravity $\mid$ ?4D $\mid$ ?CDT $\mid$ First paper to show the emergence of a 4D de Sitter universe from CDT.

## Quantum Spacetime Properties

- 2023 - Measuring the Homogeneity (or Otherwise) of the Quantum Universe $\mid$ ?2D $\mid$ ?CDT
- 2023 - Scale-invariant random geometry from mating of trees: a numerical study $\mid$ ?2D $\mid$ ?EDT
- 2022 - From Trees to Gravity $\mid$ ?2D $\mid$ ?CDT
- 2022 - Generalised spectral dimensions in non-perturbative quantum gravity $\mid$
?4D $\mid$
?CDT $\mid$
co-authored $\mid$ Published in
*Classical and Quantum Gravity***40**(2023) 125003 $\mid$ First paper on generalised spectral dimension where we studied different types of fields in CDT and their effect on the spectral dimension. - 2021 - Quantum Flatness in Two-Dimensional CDT Quantum Gravity $\mid$ ?2D $\mid$ ?CDT
- 2021 - Cosmic voids and filaments from quantum gravity $\mid$ ?4D $\mid$ ?CDT
- 2021 - Matter-driven change of spacetime topology $\mid$ ?4D $\mid$ ?CDT
- 2020 - Approximate Killing symmetries in non-perturbative quantum gravity $\mid$ ?2D $\mid$ ?CDT
- 2020 - Spectral Analysis of Causal Dynamical Triangulations via Finite Element Method $\mid$ ?2D $\mid$ ?CDT
- 2020 - Properties of dynamical fractal geometries in the model of causal dynamical triangulations $\mid$ ?3D $\mid$ ?CDT $\mid$ Toroidal topology
- 2019 - Setting the physical scale of dimensional reduction in causal dynamical triangulations $\mid$ ?4D $\mid$ ?CDT $\mid$ Aim to establish a relation between diffusion time and physical scale
- 2018 - Quantizing quantum Ricci curvature $\mid$ ?2D $\mid$ ?EDT
- 2017 - Introducing Quantum Ricci Curvature $\mid$ ?2D $\mid$ Done only in flat and non-flat case but, not in dynamical case.
- 2017 - Scaling analyses of the spectral dimension in 3-dimensional causal dynamical triangulations $\mid$ ?3D $\mid$ ?CDT
- 2016 - Comments on “Searching for a continuum limit in CDT quantum gravity” $\mid$ ?CDT
- 2016 - Searching for a continuum limit in causal dynamical triangulation quantum gravity $\mid$ ?CDT
- 2016 - Extrinsic curvature in 2-dimensional Causal Dynamical Triangulation $\mid$ ?2D $\mid$ ?CDT
- 2015 - What is dimensional reduction really telling us?
- 2015 - Wilson loops in CDT quantum gravity $\mid$ ?CDT
- 2014 - Scale-dependent homogeneity measures for causal dynamical triangulations $\mid$ ?3D $\mid$ ?CDT
- 2014 - The spectral dimension in 2D CDT gravity coupled to scalar fields $\mid$ ?2D $\mid$ ?CDT
- 2013 - Exploring Torus Universes in Causal Dynamical Triangulations $\mid$ ?3D $\mid$ ?CDT
- 2012 - Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields $\mid$ ?2D $\mid$ ?CDT
- 2009 - Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?
- 2009 - Spectral geometry as a probe of quantum spacetime $\mid$ ?3D $\mid$ ?CDT
- 2009 - On the spectral dimension of causal triangulations $\mid$ ?2D $\mid$ ?CDT
- 2007 - (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations $\mid$ ?3D $\mid$ ?CDT
- 2005 - Spectral Dimension of the Universe $\mid$ ?4D $\mid$ ?CDT $\mid$ This paper is renamed as “The Spectral Dimension of the Universe is Scale Dependent” $\mid$ First time reported the discovery of the effective dimension of quantum spacetime geometry dynamically reduces to a value near 2 on sufficiently small scales (UV), and on large scale (IR), it is equal to the topological dimension that is 4.
- 2003 - Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity $\mid$ ?2D $\mid$ ?CDT
- 1999 - On the relation between Euclidean and Lorentzian 2D quantum gravity $\mid$ ?2D $\mid$ ?EDT $\mid$ ?CDT
- 1998 - Quantum Geometry and Diffusion $\mid$ ?2D $\mid$ ?EDT
- 1998 - The Spectral Dimension of 2D Quantum Gravity $\mid$ ?2D $\mid$ ?EDT
- 1998 - Connected Correlators in Quantum Gravity $\mid$ ?2D $\mid$ ?EDT
- 1997 - The spectral dimension of the branched polymers phase of two-dimensional quantum gravity $\mid$ ?2D $\mid$ ?EDT
- 1997 - Two-Dimensional Dynamical Triangulation using the Grand-canonical Ensemble $\mid$ ?EDT
- 1997 - Quantum geometry of 2d gravity coupled to unitary matter $\mid$ ?2D $\mid$ ?EDT
- 1996 - Topology in 4D simplicial quantum gravity $\mid$ ?4D $\mid$ ?EDT
- 1996 - Quantum geometry of topological gravity $\mid$ ?4D $\mid$ ?EDT
- 1995 - Entropy estimates for simplicial quantum gravity $\mid$ ?EDT $\mid$ Not in arXiv
- 1995 - Singular Vertices and the Triangulation Space of the D-sphere $\mid$ ?EDT
- 1995 - Baby Universes in 4d Dynamical Triangulation $\mid$ ?4D $\mid$ ?EDT
- 1995 - On the fractal structure of two-dimensional quantum gravity $\mid$ ?2D $\mid$ ?EDT
- 1995 - Scaling in four dimensional quantum gravity $\mid$ ?4D $\mid$ ?EDT
- 1994 - Computational Ergodicity of $S^{4}$ $\mid$ ?4D $\mid$ ?EDT
- 1994 - Curvature and scaling in 4D dynamical triangulation $\mid$ ?4D $\mid$ ?EDT
- 1994 - On the exponential bound in four dimensional simplicial gravity $\mid$ ?4D $\mid$ ?EDT
- 1994 - On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity $\mid$ ?4D $\mid$ ?EDT
- 1986 - A Numerical Study of Discrete Euclidean Polyakov Surfaces $\mid$ ?2D $\mid$ ?EDT $\mid$ Not in arXiv
- 1985 - Diseases of triangulated random surface models, and possible cures $\mid$ ?2D $\mid$ ?EDT $\mid$ Not in arXiv

## Connections to other models

- 2023 - Critical JT Gravity $\mid$ ?2D $\mid$ ?EDT $\mid$ JT Gravity
- 2022 - CDT and Horava-Lifshitz QG in Two Dimensions $\mid$ ?2D $\mid$ ?CDT $\mid$ Horava-Lifshitz $\mid$ Book Chapter
- 2021 - Coupling Yang-Mills with Causal Dynamical Triangulations $\mid$ ?2D $\mid$ ?CDT $\mid$ Yang-Mills
- 2021 - Wormhole interaction in 2d Horava-Lifshitz quantum gravity $\mid$ ?2D $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2021 - Wormholes in 2d Horava-Lifshitz quantum gravity $\mid$ ?2D $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2020 - Compact Gauge Fields on Causal Dynamical Triangulations: a 2D case study $\mid$ ?2D $\mid$ ?CDT $\mid$ Yang-Mills
- 2017 - Dimension and Dimensional Reduction in Quantum Gravity
- 2016 - Causal dynamical triangulation of a 3D tensor model $\mid$ ?3D $\mid$ ?CDT
- 2015 - A model for emergence of space and time
- 2015 - Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations $\mid$ ?2D $\mid$ ?CDT $\mid$ Asymptotic Safety
- 2014 - Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model $\mid$ ?3D $\mid$ ?CDT $\mid$ Horava-Lifshitz $\mid$ Minisuperspace
- 2014 - A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity? $\mid$ ?2D $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2013 - Four-dimensional Causal Dynamical Triangulations and an effective transfer matrix $\mid$ ?4D $\mid$ ?CDT $\mid$ Minisuperspace
- 2013 - 2d CDT is 2d Horava-Lifshitz quantum gravity $\mid$ ?2D $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2013 - Causal dynamical triangulations and the search for a theory of quantum gravity $\mid$ ?4D $\mid$ ?CDT $\mid$ Horava-Lifshitz $\mid$ Asymptotic Safety
- 2012 - A local induced action for the noncritical string $\mid$ ?2D
- 2011 - Causal Dynamical Triangulation with Extended Interactions in 1+1 Dimensions $\mid$ ?2D $\mid$ ?CDT
- 2011 - Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2010 - CDT meets Horava-Lifshitz gravity $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2009 - Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point $\mid$ ?4D $\mid$ ?CDT $\mid$ Horava-Lifshitz
- 2008 - Imposing causality on a matrix model $\mid$ ?2D $\mid$ ?CDT $\mid$ Matrix Model
- 2003 - Renormalization of 3d quantum gravity from matrix models $\mid$ ?3D $\mid$ ?CDT $\mid$ Matrix Model
- 1999 - A new perspective on matter coupling in 2d quantum gravity $\mid$ ?2D $\mid$ ?EDT $\mid$ Liouville $\mid$ Proved the the 2D CDT is an alternative to 2D Liouville quantum gravity.
- 1998 - Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter $\mid$ ?EDT

## Phenomenology

- 2017 - From Causal Dynamical Triangulations To Astronomical Observations $\mid$ ?CDT
- 2015 - Phenomenology of Causal Dynamical Triangulations $\mid$ ?CDT
- 2005 - Counting a black hole in Lorentzian product triangulations $\mid$ ?CDT

## Books

- 2022 - Jan Ambjorn - Elementary Introduction to Quantum Geometry $\mid$ in arXiv $\mid$ ?2D $\mid$ ?EDT $\mid$ ?CDT
- 2016 - Bertrand Eynard - Counting Surfaces $\mid$ ?2D $\mid$ ?EDT
- 1997 - Jan Ambjørn, Mauro Carfora, Annalisa Marzuoli - The Geometry of Dynamical Triangulations $\mid$ in arXiv $\mid$ ?2D $\mid$ ?EDT
- 1997 - Jan Ambjørn, Bergfinnur Durhuus, Thordur Jonsson - Quantum Geometry - A Statistical Field Theory Approach $\mid$ ?2D $\mid$ ?EDT

## Theses

- 2022 Ph.D. - Dániel Németh- Studies of Critical Phenomena in Causal Dynamical Triangulations on a Torus$\mid$ ?4D $\mid$ ?CDT
- 2021 M.Sc. - Willem van der Feltz - Master coupling to two-dimensional Causal Dynamical Triangulations$\mid$ ?2D $\mid$ ?CDT
- 2021 Ph.D. - Marcus Reitz - Observables in non-perturbative quantum gravity - What to measure if space-time is quantum?
- 2021 Ph.D. - Nilas Klitgaard - New Curvatures for Quantum Gravity
- 2021 Ph.D. - Zbigniew Drogosz - New topological observables in a model of Causal Dynamical Triangulations on a torus $\mid$ ?4D $\mid$ ?CDT
- 2021 M.Sc. - Djamel van der Sluis - Statistics of spatial geometries in Causal Dynamical Triangulations in 2+1 dimensions $\mid$ ?3D $\mid$ ?CDT
- 2018 B.Sc. - Damodar Rajbhandari - An open source code for Causal Dynamical Triangulations without preferred foliation in (1+1)-dimensions
- 2017 Ph.D. - Jonah Miller - Selected Problems in Computational Gravity
- 2015 Ph.D. - Hongguang Zhang - Phase structure of 1+1 Causal Dynamical Triangulation with matter $\mid$ ?2D $\mid$ ?CDT
- 2014 Ph.D. - Jakub Gizbert-Studnicki - The effective action in four-dimensional CDT $\mid$ ?4D $\mid$ ?CDT
- 2014 M.Sc. - Scott N.A. Smith - On Causal Structure in (1 + 1)-Dimensional and (2 + 1)-Dimensional Generalised Causal Dynamical Triangulations $\mid$ ?3D $\mid$ ?GCDT
- 2014 Ph.D. - Lisa Glaser - Endeavours in Discrete Lorentzian Geometry; A thesis in five papers $\mid$ ?CDT
- 2014 Ph.D. - Yuki Sato - Space-Time Foliation in Quantum Gravity
- 2013 Ph.D. - Samo Jordan - Globally and locally causal dynamical triangulations $\mid$ ?GCDT
- 2013 M.Sc. - Ben Ruijl - Locally causal dynamical triangulations $\mid$ ?2D $\mid$ ?GCDT
- 2012 M.Sc. - Renee Hoekzema - Generalized Causal Dynamical Triangulations in two dimensions $\mid$ ?2D $\mid$ ?CDT $\mid$ Extended calculations of 1998 first CDT paper
- 2012 Ph.D. - Timothy Budd - Non-perturbative quantum gravity A conformal perspective $\mid$ ?2D $\mid$ ?EDT $\mid$ ?CDT
- 2011 M.Sc. - Alex Forcier - Introductory Causal Dynamical Triangulation $\mid$ ?2D $\mid$ ?CDT $\mid$ Elaborated calculations of 1998 first CDT paper
- 2011 Ph.D. - Mitchell Thomson - The Microcanonical Density of States and Causal Dynamical Triangulations
- 2010 Ph.D. - Andrzej Görlich - Causal Dynamical Triangulations in Four Dimensions $\mid$ ?4D $\mid$ ?CDT $\mid$ You can read the construction of initial triangulation with spherical topology $S^{4}\equiv S^{1} \times S^{3}$. $\mid$ We have time to be periodic due to numerical reason.
- 2007 Ph.D. - Dario Benedetti - Quantum Gravity from Simplices: Analytical Investigations of Causal Dynamical Triangulations $\mid$ ?2D $\mid$ ?3D $\mid$ ?4D $\mid$ ?CDT
- 2005 M.Sc. - Stefan Zohren - Analytic Results in 2D Lorentzian Quantum Gravity $\mid$ ?2D $\mid$ ?CDT $\mid$ arXiv

Permalink athttps://www.physicslog.com/physics-notes/cdt-papers

Published onApr 19, 2023

Last revised onMay 27, 2024

References

- Causal dynamical triangulation (wiki)
- Scientific American: Using Causality to Solve the Puzzle of Quantum Spacetime
- Quanta Magazine: The Physicist Who Glues Together Universes
- Hyperspace
- QG Talks at PIRSA
- QG2020 Talks at PIRSA
- Quantum Gravity Across Approaches
- Quantum Gravity and All of That
- SciTalks
- Quantum Gravity (Scholarpedia)
- Quantum Gravity Collections
- Physics beyond the Standard Model (wiki)