2D Quantum Gravity in the Proper-Time Gauge

Ryuichi Nakayama

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2D Quantum Gravity in the Proper-Time Gauge

Ryuichi Nakayama

High Energy Physics - Theory · Submitted 20 Dec 1993

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The authors' main claim A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.20 · mentions code or data availability 0.02.

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A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation. The constraint $T_{01}=0$ is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths $l_1, l_2$ of the boundaries, the proper time $T$ and a non-negative integer $m$ associated with winding modes around the boundaries.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation.	contribution 0.67	0.93	0.65	asserted 1.00
s1	The constraint $T_{01}=0$ is solved and used to reduce the problem of field theory to that of quantum mechanics.	method 0.99	0.86	0.11	asserted 1.00
s2	This reduction can also be proved by using a conformal Ward identity.	method 0.71	0.48	0.06	asserted 0.83
s3	The amplitude depends on the lengths $l_1, l_2$ of the boundaries, the proper time $T$ and a non-negative integer $m$ associated with winding modes around the boundaries.	result 0.99	0.87	0.20	asserted 1.00

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Original abstract

A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation. The constraint $T_{01}=0$ is solved and used to reduce the problem of field theory to that of quantum mechanics. This reduction can also be proved by using a conformal Ward identity. The amplitude depends on the lengths $l_1, l_2$ of the boundaries, the proper time $T$ and a non-negative integer $m$ associated with winding modes around the boundaries.

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References

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
hep-th 1998-05 accept novelty 8.0 of 10

Restricting the two-dimensional gravity path integral to causally ordered triangulations gives an exactly solvable theory in a different universality class from Liouville gravity, unless spatial topology change is allowed.
Nonperturbative Quantum Gravity
hep-th 2012-03 conditional novelty 3.0 of 10

Causal Dynamical Triangulations, reviewed in full, produce a four-dimensional de Sitter-like phase whose second-order boundary is presented as a candidate ultraviolet fixed point for quantum gravity.
Nonperturbative sum over topologies in 2D Lorentzian quantum gravity
hep-th 2006-03 conditional novelty 2.0 of 10

In a 1+1 dimensional causal quantum gravity model, summing over all spacetime topologies is well-defined and yields a finite density of infinitesimal wormholes that decreases the effective cosmological constant.

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9 arXiv papers cite this in 22 sentences

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Papers citing it · 17 sentences without a confident label

Builds on it 1 paper

Using a spectral decomposition, the propagator can be expressed in terms of a basis $ψ_n(ℓ)$ of eigenfunctions and associated eigenvalues $E_n$ of $Ĥ$: [equation] This approach was used in [ref] ; we generalize the computation therein to the case of varied factor ordering.

Anomalous diffusion and factor ordering in (1+1)-dimensional Lorentzian quantum gravity · Amplitude for propagation from a Big Bang · 0.83

Uses its method or tool 1 paper

To investigate how factor ordering of the canonically quantized Wheeler-DeWitt operator affects predictions for quantum geometry, we use a reduced model of Lorentzian (1+1)-dimensional gravity as in [ref] , where the constructions involved are more rigorously understood than in the physical (3+1)-dimensional case.

Anomalous diffusion and factor ordering in (1+1)-dimensional Lorentzian quantum gravity · Introduction · 0.91

Cites it as background 2 papers

The other universality class is that of Lorentzian or causal models, characterized by $d_H = 2$, $d_S = 2$ and $γ = 1/2$ and contains 2D gravity in proper-time gauge [ref] , 2D CDT [ref] and the uniform infinite planar tree [ref] .

What is the Curvature of 2D Euclidean Quantum Gravity? · The three geometric ensembles · 0.90
A Hamiltonian operator and cylinder (or loop-loop) amplitude emerge (see [ref] for a review) which reproduce results first obtained in [ref] by a proper-time gauge calculation in 1+1D continuum gravity.

The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations · Introduction · 0.89

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