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Constructing Gravitational Dimensions
High Energy Physics - Theory · Submitted 13 Mar 2003
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It dictates an intricate set of interactions among various fields which conspire to soften the strongest scattering amplitudes and allow for a local continuum limit.
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The abstract, sentence by sentence
It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with multiple interacting massive gravitons. It is actually very difficult to construct discrete gravitational dimensions which have a local continuum limit. In fact, any model with only nearest neighbor interactions is doomed. If we could find a non-linear extension for the Fierz-Pauli Lagrangian for a graviton of mass mg which does not break down until the scale Lambda_2=(mg Mpl)^(1/2), this could be used to construct a large class of models whose continuum limit is local in the extra dimension. But this is shown to be impossible: a theory with a single graviton must break down by Lambda_3 = (mg^2 Mpl)^(1/3). Next, we look at how the discretization prescribed by the truncation of the KK tower of an honest extra diemsinon rasies the scale of strong coupling. It dictates an intricate set of interactions among various fields which conspire to soften the strongest scattering amplitudes and allow for a local continuum limit. A number of canditate symmetries associated with locality in the discretized dimension are also discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. | background 0.91 | 0.04 | 0.03 | speculative 0.45 |
| s1 | Here, this problem is approached from the ground up by considering theories with multiple interacting massive gravitons. | contribution 0.54 | 0.75 | 0.03 | asserted 0.96 |
| s2 | It is actually very difficult to construct discrete gravitational dimensions which have a local continuum limit. | background 0.53 | 0.30 | 0.13 | asserted 0.99 |
| s3 | In fact, any model with only nearest neighbor interactions is doomed. | result 0.95 | 0.56 | 0.13 | asserted 1.00 |
| s4 | If we could find a non-linear extension for the Fierz-Pauli Lagrangian for a graviton of mass mg which does not break down until the scale Lambda_2=(mg Mpl)^(1/2), this could be used to construct a large class of models whose continuum limit is local in the extra dimension. | gap 0.39 | 0.14 | 0.10 | hedged possibility 0.98 |
| s5 | But this is shown to be impossible: a theory with a single graviton must break down by Lambda_3 = (mg^2 Mpl)^(1/3). | result 0.99 | 0.77 | 0.34 | asserted 1.00 |
| s6 | Next, we look at how the discretization prescribed by the truncation of the KK tower of an honest extra diemsinon rasies the scale of strong coupling. | contribution 0.51 | 0.51 | 0.06 | asserted 0.84 |
| s7 | It dictates an intricate set of interactions among various fields which conspire to soften the strongest scattering amplitudes and allow for a local continuum limit. | result 0.55 | 0.52 | 0.25 | asserted 1.00 |
| s8 | A number of canditate symmetries associated with locality in the discretized dimension are also discussed. | contribution 0.95 | 0.68 | 0.05 | asserted 0.67 |
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The paper
Original abstract
It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with multiple interacting massive gravitons. It is actually very difficult to construct discrete gravitational dimensions which have a local continuum limit. In fact, any model with only nearest neighbor interactions is doomed. If we could find a non-linear extension for the Fierz-Pauli Lagrangian for a graviton of mass mg which does not break down until the scale Lambda_2=(mg Mpl)^(1/2), this could be used to construct a large class of models whose continuum limit is local in the extra dimension. But this is shown to be impossible: a theory with a single graviton must break down by Lambda_3 = (mg^2 Mpl)^(1/3). Next, we look at how the discretization prescribed by the truncation of the KK tower of an honest extra diemsinon rasies the scale of strong coupling. It dictates an intricate set of interactions among various fields which conspire to soften the strongest scattering amplitudes and allow for a local continuum limit. A number of canditate symmetries associated with locality in the discretized dimension are also discussed.
Human review
References
How the literature uses it
24 arXiv papers cite this in 50 sentences
Papers citing it · 40 sentences without a confident label
Contests it 1 paper
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Thus, the total amplitude in the truncated theory grows like $O(s^5)$ – not like $O(s^3)$ as [ref] had suggested.] which lead to the total amplitude's growing only like $s$.
Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States Grow Only as ${\cal O}(s)$ · Orbifolded Torus · contest 0.81
Uses its method or tool 3 papers
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We can graphically represent a theory with $$-metrics and the interaction term [ref] by drawing a “theory graph," (or gravitational quiver diagram) following [ref] .
Interacting Spin-2 Fields · The interaction terms · 0.94
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However, we here impose the correct normalisations, anticipating that this will give the correct kinetic structure.]: [equation] After this rescaling, and remembering the overall factor of $M_P^2 m^2$ in front of the potential in [ref], the general interaction term ${n_h, n_A, n_ϕ}$ involving $n_ϕ$ fields $ϕ$, $n_A$ fields $A_μ$ and $n_h$ fields $h_μν$ is given by [ref] {n_h, n_A, n_ϕ} ≡Λ_λ^4-n_h-2n_A-3n_ϕ ĥ^n_h (∂Â)^n_A (∂^2 ϕ̂)^n_ϕ, where one can read off that the associated interaction scale is [equation] where $n_h + n_A + n_ϕ ≥3$.
On strong coupling scales in (minimal) massive gravity · Interaction scales · 0.80
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Rather than starting directly with a Kaluza–Klein decomposition (discretization in Fourier space), we perform instead a discretization in real space, known as “deconstruction” of five-dimensional gravity [ref] .
Massive Gravity · Deconstruction · 0.90
Cites it as support 1 paper
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It is avoided by a subtle cancellation between the contributions of the full KK tower which restores perturbative unitarity of tree-level amplitudes up to the Planck scale [ref] .
Gravity-Matter Sum Rules in models with a single extra-dimension · Introduction · 0.98
Cites it as background 4 papers
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The unitarity of four-dimensional amplitudes coming from a five-dimensional compactification has been studied in Refs. [ref] .
Unitarization from Geometry · General relativity · 0.97
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Deconstruction actually has its origins in non-gravitational gauge theories [ref] , but the basic procedure applies equally well to gravity too [ref] ; it is related to the more standard KK procedure, whereby one integrates out the extra dimensions instead of discretising them, by a discrete Fourier transform [ref] .
A new look at multi-gravity and dimensional deconstruction · Introduction · 0.94
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This high energy scaling is expected in a naive Fierz-Pauli theory [ref] or extensions like bigravity/dRGT gravity [ref] [At high energies the scattering amplitudes of massive gravitons ($GG→GG$) in the Fierz-Pauli theory grows as $s^5/(M_G^8M_Pl^2)$, which can be estimated from power counting arguments [ref] .
Graviton-photon production with a massive spin-2 particle · Introduction · 0.83
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