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One Loop Beta Functions in Topologically Massive Gravity
High Energy Physics - Theory · Submitted 15 Feb 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point.
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The abstract, sentence by sentence
We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that \nu, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. | contribution 1.00 | 0.96 | 0.08 | asserted 0.97 |
| s1 | We find that \nu, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. | result 1.00 | 0.97 | 0.28 | asserted 1.00 |
| s2 | The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point. | result 1.00 | 0.91 | 0.53 | asserted 1.00 |
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The paper
Original abstract
We calculate the running of the three coupling constants in cosmological, topologically massive 3d gravity. We find that \nu, the dimensionless coefficient of the Chern-Simons term, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on \nu, and for any positive \nu there exist both a trivial and a nontrivial fixed point.
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References
How the literature uses it
23 arXiv papers cite this in 41 sentences
Papers citing it · 22 sentences without a confident label
Uses its method or tool 3 papers
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We follow Ref. [ref] and suppress the contribution of the field modes with momenta lower than $k$ by modifying the low momentum end of the propagator and leaving all the interactions unaffected.
Beta Function and Asymptotic Safety in Three-dimensional Higher Derivative Gravity · Wilsonian method for renormalization group · 1.00
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We find L_gf=-1/2a [ξ̂^μ(+2Λ) ξ̂_μ-4/9 η̂(+3Λ)η̂+3b-1/9 h √((+3Λ))η̂-(3b-1)^2/144hh ], L_gh=- V̅^μ(+2Λ) V_μ+ Ŝ̅̂(3-b/2+4Λ)Ŝ, where we have defined [ref] C_μ≡V_μ+∇_μS, Ŝ = √() S, ∇_μV^μ=0, C̅_μ≡V̅_μ+∇_μS̅, Ŝ̅̂ = √() S̅, ∇_μV̅^μ=0.
A Complete Classification of Higher Derivative Gravity in 3D and Criticality in 4D · Theory around maximally symmetric spacetimes · 0.97
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Alternatively, we can compute the traces in Eq. ([ref]) by summing directly the corresponding functions of the eigenvalues of the Laplacian on the sphere [ref] TrW(Δ+E)=∑_ℓM_ℓW(λ_ℓ+E) ,
Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization · Spectral sum approach for $d=4$ · 1.00
Compares with it 5 papers
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These equations are exactly of the same form as in pure gravity with cosmological constant and in the topological gravity [ref] .$
Beta Function and Asymptotic Safety in Three-dimensional Higher Derivative Gravity · Evaluation of the functional traces · 0.96
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This is the same as in bosonic three-dimensional Einstein gravity [ref] .
Beta Functions of Topologically Massive Supergravity · The Beta Functions of Pure Supergravity · 0.99
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The RG flows studied in [ref] and [ref] did not preserve the special subspaces, in those cases.
Quantization and fixed points of non-integrable Weyl theory · Introduction · 0.85
Cites it as background 6 papers
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This philosophy is behind many of the approaches to 3-dimensional quantum gravity that emerged in the past five years (see [ref] for an incomplete selection of references).
Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings · Introduction · 1.00
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The renormalization group (RG) of this “topologically massive gravity” has been studied in [ref] , and its supergravity extension in [ref] .
Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions · Introduction · 0.92
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For such discussions for higher derivative gravity, see [ref] .
Renormalization of Higher Derivative Quantum Gravity Coupled to a Scalar with Shift Symmetry · Introduction · 0.97
What it cites · 14 sentences without a confident label
Uses the method or tool of 3 papers
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We will follow [ref] and use the background field method, thereby effectively replacing the dynamical metric $g_μν$ by a spin two field $h_μν$ propagating in a fixed but unspecified background $g̅_μν$.
Nonperturbative Evolution Equation for Quantum Gravity · Wilsonian Method For Computing the RGE · 1.00
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In order to be able to perform the summations in closed form we will use the “optimized” cutoff $R_k(z)=(k^2-|z|)θ(k^2-|z|)$ [ref] .
Optimised Renormalisation Group Flows · The Cutoff · 1.00
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These can be evaluated using standard methods (see for example Appendix B in [ref] ) and are listed in the table.
Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation · Gravity without CS term · 0.92
Compares with 1 paper
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These results agree, for $α=1$, with those reported in Section IV D of [ref] .
Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation · Gravity without CS term · 1.00
Cites as background 8 papers
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In four dimensional gravity, a nontrivial FP has been found in the leading order of the $2+ϵ$ expansion [ref] and of a $1/N$ expansion [ref] , in perturbation theory [ref] and in a variety of truncations of an exact RG equation [ref] also in the presence of matter [ref] .
Ultraviolet properties of f(R)-Gravity · Asymptotic safety and higher derivative terms · 0.87
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In four dimensional gravity, a nontrivial FP has been found in the leading order of the $2+ϵ$ expansion [ref] and of a $1/N$ expansion [ref] , in perturbation theory [ref] and in a variety of truncations of an exact RG equation [ref] also in the presence of matter [ref] .
Asymptotic safety in higher-derivative gravity · Asymptotic safety and higher derivative terms · 0.87
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In four dimensional gravity, a nontrivial FP has been found in the leading order of the $2+ϵ$ expansion [ref] and of a $1/N$ expansion [ref] , in perturbation theory [ref] and in a variety of truncations of an exact RG equation [ref] also in the presence of matter [ref] .
Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity · Asymptotic safety and higher derivative terms · 0.87
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