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Analytic Results in 2D Causal Dynamical Triangulations: A Review
High Energy Physics - Theory · Submitted 25 Sep 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity.
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The abstract, sentence by sentence
We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity whose ground state describes a two-dimensional "universe" completely governed by quantum fluctuations. One observes that two-dimensional Lorentzian and Euclidean quantum gravity are distinct. In the second part of the review we address the question of how to incorporate a sum over space-time topologies in the gravitational path integral. It is shown that, provided suitable causality restrictions are imposed on the path integral histories, there exists a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of CDT. A complete analytical solution of the quantum continuum dynamics is obtained uniquely by means of a double scaling limit. We show that in the continuum limit there is a finite density of infinitesimal wormholes. Remarkably, the presence of wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the context of a Euclidean path integral formulation of four-dimensional quantum gravity in the continuum. In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). | background 0.80 | 0.42 | 0.04 | asserted 0.78 |
| s1 | In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity whose ground state describes a two-dimensional "universe" completely governed by quantum fluctuations. | result 0.82 | 0.44 | 0.26 | asserted 1.00 |
| s2 | One observes that two-dimensional Lorentzian and Euclidean quantum gravity are distinct. | result 0.71 | 0.32 | 0.05 | asserted 1.00 |
| s3 | In the second part of the review we address the question of how to incorporate a sum over space-time topologies in the gravitational path integral. | contribution 0.60 | 0.35 | 0.04 | unclear 0.73 |
| s4 | It is shown that, provided suitable causality restrictions are imposed on the path integral histories, there exists a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of CDT. | result 0.79 | 0.83 | 0.33 | asserted 0.99 |
| s5 | A complete analytical solution of the quantum continuum dynamics is obtained uniquely by means of a double scaling limit. | result 0.73 | 0.81 | 0.22 | asserted 1.00 |
| s6 | We show that in the continuum limit there is a finite density of infinitesimal wormholes. | result 1.00 | 0.88 | 0.14 | asserted 1.00 |
| s7 | Remarkably, the presence of wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the context of a Euclidean path integral formulation of four-dimensional quantum gravity in the continuum. | interpretation 0.78 | 0.79 | 0.15 | asserted 0.96 |
| s8 | In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity. | contribution 0.61 | 0.56 | 0.24 | asserted 0.61 |
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Original abstract
We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity whose ground state describes a two-dimensional "universe" completely governed by quantum fluctuations. One observes that two-dimensional Lorentzian and Euclidean quantum gravity are distinct. In the second part of the review we address the question of how to incorporate a sum over space-time topologies in the gravitational path integral. It is shown that, provided suitable causality restrictions are imposed on the path integral histories, there exists a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of CDT. A complete analytical solution of the quantum continuum dynamics is obtained uniquely by means of a double scaling limit. We show that in the continuum limit there is a finite density of infinitesimal wormholes. Remarkably, the presence of wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the context of a Euclidean path integral formulation of four-dimensional quantum gravity in the continuum. In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity.
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References
How the literature uses it
4 arXiv papers cite this in 6 sentences
Papers citing it · 2 sentences without a confident label
Compares with it 1 paper
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On the basis of the apparent stability observed, we have performed a fit of all determinations to a constant value, obtaining $ν= 0.496(7)$ ($χ^2 / dof = 9.1/9$), which is compatible with the value expected in the pure gravity case ($ν= 1/2$) (see [ref] ).
Coupling Yang-Mills with Causal Dynamical Triangulations · Gravity related observables · 0.86
Cites it as support 1 paper
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Furthermore, there is independent evidence for asymptotic safety coming from recent lattice simulations, causal dynamical triangulations [ref] .
Extra Dimensions and their Ultraviolet Completion · Fixed-point gravity · 0.99
Cites it as background 2 papers
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The detailed way of encoding of geometry in a simplicial manifold is as follows (cf. [ref] , [ref] ).
Analysis of the Semiclassical Solution of CDT · Method of dynamical triangulations · 0.88
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Also, in the continuum 1+1 dimensional model of Causal Dynamical Triangulations, one can calculate a Hamiltonian governing the (proper) time evolution of a universe of some initial size or length [ref] .
A one-particle time of arrival operator for a free relativistic spin-0 charged particle in (1+1) dimensions · Conclusion · 0.95
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