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Curvature Correlators in Nonperturbative 2D Lorentzian Quantum Gravity
High Energy Physics - Theory · Submitted 26 Apr 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes.
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The abstract, sentence by sentence
Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. This work paves the way for an analogous investigation in higher dimensions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. | background 1.00 | 0.03 | 0.01 | asserted 1.00 |
| s1 | However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. | gap 0.95 | 0.04 | 0.02 | asserted 1.00 |
| s2 | We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. | contribution 1.00 | 0.95 | 0.06 | asserted 0.99 |
| s3 | It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. | method 0.99 | 0.58 | 0.03 | asserted 1.00 |
| s4 | We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. | result 1.00 | 0.97 | 0.90 | asserted 0.82 |
| s5 | This work paves the way for an analogous investigation in higher dimensions. | future work 0.99 | 0.25 | 0.03 | asserted 0.66 |
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The paper
Original abstract
Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. This work paves the way for an analogous investigation in higher dimensions.
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References
How the literature uses it
3 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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Observables are given by Hermitian functional operators that are subject to diffeomorphism constraints (see [ref] for a recent discussion).
Remarks on 2D quantum cosmology · Matter contribution · 0.81
What it cites · 66 sentences without a confident label
Builds on 2 papers
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Following earlier work in 2D CDT on the average quantum Ricci curvature as a function of a local coarse-graining scale [ref] , the so-called curvature profile [ref] , we will investigate here its two-point correlator by a numerical analysis.
Curvature profiles for quantum gravity · Theoretical and computational set-up · 0.96
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Following earlier work in 2D CDT on the average quantum Ricci curvature as a function of a local coarse-graining scale [ref] , the so-called curvature profile [ref] , we will investigate here its two-point correlator by a numerical analysis.
Quantum Flatness in Two-Dimensional CDT Quantum Gravity · Theoretical and computational set-up · 0.96
Uses the method or tool of 6 papers
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In terms of these ingredients, the formal path integral ([ref]) takes the explicit form [equation] where we have used the Wick rotation of CDT (analytic continuation $α↦ -α$ in the lower-half complex plane [ref] ) to obtain a real partition function $Z_CDT$, which is easier to work with computationally and will be the setting for the work presented here.
Dynamically Triangulating Lorentzian Quantum Gravity · Theoretical and computational set-up · 0.81
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In terms of these ingredients, the formal path integral ([ref]) takes the explicit form [equation] where we have used the Wick rotation of CDT (analytic continuation $α↦ -α$ in the lower-half complex plane [ref] ) to obtain a real partition function $Z_CDT$, which is easier to work with computationally and will be the setting for the work presented here.
Nonperturbative Quantum Gravity · Theoretical and computational set-up · 0.81
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In the present work, we have used a slight variant of the criterion in [ref] to find a set ${δ_max }$ of such thresholds, see [ref] for details.
Quantum Flatness in Two-Dimensional CDT Quantum Gravity · Quantum Ricci curvature · 0.99
Compares with 1 paper
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The joint enveloping curve of the curvature profile increases, with a decreasing slope for growing $δ$, similar to what was observed in [ref] , and indicating the presence of negative curvature.
Quantum Flatness in Two-Dimensional CDT Quantum Gravity · Quantum Ricci curvature · 0.96
Cites as background 11 papers
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The setting for our investigation of curvature correlators is the two-dimensional Lorentzian gravitational path integral, regularized in terms of CDT, which was first defined and solved analytically in [ref] .
Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change · Theoretical and computational set-up · 0.80
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We will summarize its essential properties below, and refer to [ref] for further technical details.
Nonperturbative Quantum Gravity · Theoretical and computational set-up · 0.97
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We will summarize its essential properties below, and refer to [ref] for further technical details.
Dynamically Triangulating Lorentzian Quantum Gravity · Theoretical and computational set-up · 0.97
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