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Ultraviolet Stable Fixed Point and Scaling Relations in 2+$\epsilon$ Dimensional Quantum Gravity
High Energy Physics - Theory · Submitted 23 Mar 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range $0~<~c~<~25$.
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The abstract, sentence by sentence
We formulate a renormalizable quantum gravity in $2+\epsilon$ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range $0~<~c~<~25$. This may imply the existence of consistent quantum gravity theory in 3 and 4 dimensions. We compute the scaling dimensions of the relevant operators in the theory at the ultraviolet fixed point. We obtain a scaling relation between the cosmological constant and the gravitational constant, which is crucial for searching for the continuum limit in the constructive approach to quantum gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We formulate a renormalizable quantum gravity in $2+\epsilon$ dimensions by generalizing the nonlinear sigma model approach to string theory. | method 0.54 | 0.94 | 0.07 | asserted 1.00 |
| s1 | We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range $0~<~c~<~25$. | result 1.00 | 0.95 | 0.50 | asserted 0.99 |
| s2 | This may imply the existence of consistent quantum gravity theory in 3 and 4 dimensions. | interpretation 1.00 | 0.19 | 0.28 | hedged possibility 1.00 |
| s3 | We compute the scaling dimensions of the relevant operators in the theory at the ultraviolet fixed point. | contribution 0.79 | 0.96 | 0.06 | asserted 1.00 |
| s4 | We obtain a scaling relation between the cosmological constant and the gravitational constant, which is crucial for searching for the continuum limit in the constructive approach to quantum gravity. | result 0.96 | 0.95 | 0.23 | asserted 1.00 |
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The paper
Original abstract
We formulate a renormalizable quantum gravity in $2+\epsilon$ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range $0~<~c~<~25$. This may imply the existence of consistent quantum gravity theory in 3 and 4 dimensions. We compute the scaling dimensions of the relevant operators in the theory at the ultraviolet fixed point. We obtain a scaling relation between the cosmological constant and the gravitational constant, which is crucial for searching for the continuum limit in the constructive approach to quantum gravity.
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References
How the literature uses it
24 arXiv papers cite this in 26 sentences
Papers citing it · 15 sentences without a confident label
Uses its method or tool 3 papers
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To this end, it is useful to employ an $ϵ$-expansion of the effective action about $D = 2$, along the lines of [ref] and then try to extend the results to $D=4$.
String Tension between de Sitter vacua and Curvature Corrections · Existence of de Sitter vacua · 0.84
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To this end, we first perform an $ϵ$-expansion around two spacetime dimensions, along the lines of [ref] , finding a closed-form solution to leading order in $ϵ$ without truncations, whose UV-behavior is governed by a non-Gaussian fixed point (NGFP) with a positive value $g_∗>0$ of the (dimensionless) Newton coupling.
Cosmological $\alpha'$-corrections from the functional renormalization group · Introduction · 0.97
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Alternatively, one may use an exponential split as advocated in [ref] (see also [ref] ) where the background field is split off the quantum field multiplicatively according to g_μν = g̅_μλ (exph)^λ_ν≡g̅_μν+ h_μν + 1/2 h_μτ h^τ_ ν +O(h^3) .
Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface · Functional Renormalisation · 0.91
Cites it as background 8 papers
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There is a series of papers for the study on the $D=(2+ϵ)$ EH action exploiting the renormalization theory [ref] .
Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric · Introduction · 0.98
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Many calculations rely on a so-called linear split or parameterisation, [equation] More recently, other types of parameterisation have been studied [ref] , the exponential split [equation] which plays a distinguished role in two-dimensional quantum gravity [ref] , and in general has the virtue of being a one-to-one mapping between metrics $g$ and symmetric fluctuation tensors $h$ [ref] .
Infinite order quantum-gravitational correlations · Functions of the fluctuation field · 0.91
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Other perturbative approaches frequently rely on renormalizing two-dimensional gravity [ref] , which requires careful distinction of poles from kinematic poles that arise from the propagator due to the topological nature of gravity in $d = 2$ [ref] .
The perturbative Ricci flow in gravity · Introduction · 0.89
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