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Compact hyperbolic extra dimensions: a M-theory solution and its implications for the LHC
High Energy Physics - Theory · Submitted 9 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The combination of a gap `a la Randall-Sundrum and the topology of an internal Riemann surface allows a geometrical solution to the hierarchy problem that does not require light Kaluza--Klein modes.
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The abstract, sentence by sentence
We study M-theory solutions involving compact hyperbolic spaces. The combination of a gap `a la Randall-Sundrum and the topology of an internal Riemann surface allows a geometrical solution to the hierarchy problem that does not require light Kaluza--Klein modes. We comment on the consequences of such a compactification for LHC physics.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study M-theory solutions involving compact hyperbolic spaces. | contribution 0.97 | 0.88 | 0.06 | asserted 0.87 |
| s1 | The combination of a gap `a la Randall-Sundrum and the topology of an internal Riemann surface allows a geometrical solution to the hierarchy problem that does not require light Kaluza--Klein modes. | result 0.84 | 0.72 | 0.72 | asserted 0.97 |
| s2 | We comment on the consequences of such a compactification for LHC physics. | interpretation 0.68 | 0.58 | 0.12 | unclear 0.92 |
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The paper
Original abstract
We study M-theory solutions involving compact hyperbolic spaces. The combination of a gap `a la Randall-Sundrum and the topology of an internal Riemann surface allows a geometrical solution to the hierarchy problem that does not require light Kaluza--Klein modes. We comment on the consequences of such a compactification for LHC physics.
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References
How the literature uses it
17 arXiv papers cite this in 25 sentences
Papers citing it · 14 sentences without a confident label
Uses its data or values 1 paper
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So from pages 9 to 12 and 16 to 17 of [ref] , it seems likely that in this approximation, the lightest massive modes of $s_μν$ will have intrinsic mass $m̅ = 3$ [ref] , and from pages 42 to 43 of [ref] , their masses as seen on the HW boundary will be $m = 3 A/B$, where $A$ and $B$ are the constants in the metric ansatz ([ref]).
Improvement of a provisional solution of the quantum-corrected field equations of d = 11 supergravity on flat R^4 times a compact hyperbolic 7-manifold, and modes that decay along the beam line outside the interaction region at the LHC · The Kaluza-Klein modes of the metric · 0.87
Cites it as support 2 papers
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Compactifications based on hyperbolic orbifolds gather a large number of properties that are useful for these problems, like a Dirac spectrum chiral zero modes, a mass gap with the KK modes, discrete residual symmetries for the stability of dark matter, and interesting cosmological constructions [ref] .
Hyperbolic extra-dimensions in particle physics and beyond · Future extensions · 1.00
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The volume grows exponentially with the ratio $l_G/l_c$, allowing a natural solution to the hierarchy problem [ref] . * Typical mass spectra for the Kaluza-Klein (KK) reduction of these spaces feature a mass gap similar to the one present in Randall-Sundrum models [ref] , therefore allowing for a solution to the hierarchy problem that does not require light KK modes [ref] . * When the extra compact space is negatively-curved, rather than flat, the dynamics of the very early universe alleviate standard cosmological problems, allowing to account for the current homogeneity and flatness of the universe [ref] . * Finite volume hyperbolic manifolds of dimension greater than two have the remarkable property of rigidity (Mostow's theorem [ref] ): geometrical quantities as the length of its shortest closed geodesics, the volume, etc. are topological invariants.
Towards Kaluza-Klein Dark Matter on Nilmanifolds · Introduction · 0.99
Cites it as background 8 papers
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A less known approach is the compactification of $q ≥2$ spacelike extra dimension on a compact hyperbolic manifold with a large genus (number of holes) proposed in 2000 in Ref. [ref] (see also Ref. [ref] ).
Compactified Spacelike Extra Dimension & Brane-Higgs Field · Introduction · 0.90
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The manifold with $λ_i>0$ is a sphere $S^2$, $λ_i=0$ is a torus $T^2$, and $λ_i<0$ is a compact hyperbolic manifold $H^2/Γ$ [ref] .
Three-generation solutions of equations of motion in heterotic supergravity · Curvatures and gauge field configurations · 0.90
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A less known approach is the compactification of $q ≥2$ spacelike extra dimension on a compact hyperbolic manifold with a large genus (number of holes) proposed in 2000 in Ref. [ref] (see also Ref. [ref] ).
Large Star/Rose Extra Dimension with Small Leaves/Petals · Introduction · 0.96
What it cites
Compares with 1 paper
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It is instructive to compare our case with the well known extra dimensional scenarios, e.g., add [ref] , rs [ref] and ued [ref] (see also [ref] ) since some of the features are common while others are quite distinctive.
Split-UED and Dark Matter · Implications for the LHC and beyond · 0.99
Cites as background 3 papers
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In this paper we consider compact hyperbolic spaces which have been less intensively studied in physics so far [ref] but enjoy several interesting mathematical properties (see [ref] for a mathematical introduction).
Simple de Sitter Solutions · Introduction · 0.83
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In this paper we consider compact hyperbolic spaces which have been less intensively studied in physics so far [ref] but enjoy several interesting mathematical properties (see [ref] for a mathematical introduction).
A bulk inflaton from large volume extra dimensions · Introduction · 0.83
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In this paper we consider compact hyperbolic spaces which have been less intensively studied in physics so far [ref] but enjoy several interesting mathematical properties (see [ref] for a mathematical introduction).
Compactification on negatively curved manifolds · Introduction · 0.83
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