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Causal Dynamical Triangulations without Preferred Foliation
High Energy Physics - Theory · Submitted 20 May 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This suggests that the preferred foliation normally used in CDT is not a crucial (albeit convenient) part of its background structure.
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The abstract, sentence by sentence
We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties, but do not have a preferred proper-time foliation. An extensive numerical study of the associated nonperturbative path integral in 2+1 dimensions shows that it can nevertheless reproduce the emergence of an extended de Sitter universe on large scales, a key feature of CDT quantum gravity. This suggests that the preferred foliation normally used in CDT is not a crucial (albeit convenient) part of its background structure.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties, but do not have a preferred proper-time foliation. | contribution 1.00 | 0.88 | 0.15 | asserted 1.00 |
| s1 | An extensive numerical study of the associated nonperturbative path integral in 2+1 dimensions shows that it can nevertheless reproduce the emergence of an extended de Sitter universe on large scales, a key feature of CDT quantum gravity. | result 0.99 | 0.94 | 0.19 | asserted 0.63 |
| s2 | This suggests that the preferred foliation normally used in CDT is not a crucial (albeit convenient) part of its background structure. | interpretation 1.00 | 0.52 | 0.83 | hedged possibility 1.00 |
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The paper
Original abstract
We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties, but do not have a preferred proper-time foliation. An extensive numerical study of the associated nonperturbative path integral in 2+1 dimensions shows that it can nevertheless reproduce the emergence of an extended de Sitter universe on large scales, a key feature of CDT quantum gravity. This suggests that the preferred foliation normally used in CDT is not a crucial (albeit convenient) part of its background structure.
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References
How the literature uses it
36 arXiv papers cite this in 58 sentences
Papers citing it · 52 sentences without a confident label
Builds on it 1 paper
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Here we propose a generalization of these conditions [ref] to four dimensions.
Complex actions and causality violations: Applications to Lorentzian quantum cosmology · Local causality conditions · 1.00
Cites it as support 1 paper
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Then, Ref. [ref] provided direct evidence that the CDT results are independent of the spacetime foliation.
Planck-scale dimensional reduction without a preferred frame · Introduction · 0.99
Cites it as background 4 papers
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A less strict version [ref] imposes more directly a regular light cone structure (all spacetime points carry exactly one future-directed light cone and exactly one past-directed light cone) without an obvious slicing into hypersurfaces.
Causal structure and light-conical singularities in Lorentzian simplicial quantum gravity · Introduction · 0.80
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Whether or not it assumes the role of a physically distinguished notion of time in the continuum limit of the theory is not clear a priori.[A generalization of CDT quantum gravity, which does not have a distinguished time-slicing, has recently been investigated in 2+1 dimensions [ref] .] The above-mentioned matching of CDT volume profiles to continuum de Sitter universes certainly suggests that an appropriately rescaled version of $t$ can be identified with proper time on large scales and “on average" in this limit.
Exploring Torus Universes in Causal Dynamical Triangulations · Causal dynamical triangulations in 2+1 dimensions · 0.91
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Recently a modification of CDT that circumvents the strict foliation has been proposed [ref] .
Endeavours in Discrete Lorentzian Geometry; A thesis in five papers · The road forward in CDT · 0.86
What it cites · 5 sentences without a confident label
Cites as background 2 papers
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This is arguably the case for “Quantum Gravity from Causal Dynamical Triangulations (CDT)" [ref] , a nonperturbative implementation of the (formal) gravitational path integral [equation] where $S_EH[g]$ denotes the Einstein-Hilbert action as functional of the four-metric $g_μν$.
Nonperturbative Quantum Gravity · Quantum gravity and background independence · 0.94
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Next, we have to face the fact that getting rid of a preferred notion of time we also lose direct access to the average “volume profile" (two-volume $N_2$ as a function of time), the large-scale observable instrumental in connecting CDT to a de Sitter minisuperspace cosmology [ref] .
Spectral geometry as a probe of quantum spacetime · CDT without foliation: numerical set-up · 0.88
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