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Dynamical Decompactification and Three Large Dimensions
High Energy Physics - Theory · Submitted 6 Aug 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this sense the Brandenberger-Vafa mechanism is operative.
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The abstract, sentence by sentence
We study string gas dynamics in the early universe and seek to realize the Brandenberger - Vafa mechanism - a goal that has eluded earlier works - that singles out three or fewer spatial dimensions as the number which grow large cosmologically. Considering wound string interactions in an impact parameter picture, we show that a strong exponential suppression in the interaction rates for d > 3 spatial dimensions reflects the classical argument that string worldsheets generically intersect in at most four spacetime dimensions. This description is appropriate in the early universe if wound strings are heavy - wrapping long cycles - and diluted. We consider the dynamics of a string gas coupled to dilaton-gravity and find that a) for any number of dimensions the universe generically stays trapped in the Hagedorn regime and b) if the universe fluctuates to a radiation regime any residual winding modes are diluted enough so that they freeze-out in d > 3 large dimensions while they generically annihilate for d = 3. In this sense the Brandenberger-Vafa mechanism is operative.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study string gas dynamics in the early universe and seek to realize the Brandenberger - Vafa mechanism - a goal that has eluded earlier works - that singles out three or fewer spatial dimensions as the number which grow large cosmologically. | contribution 0.61 | 0.49 | 0.19 | asserted 0.41 |
| s1 | Considering wound string interactions in an impact parameter picture, we show that a strong exponential suppression in the interaction rates for d > 3 spatial dimensions reflects the classical argument that string worldsheets generically intersect in at most four spacetime dimensions. | result 0.73 | 0.88 | 0.15 | asserted 1.00 |
| s2 | This description is appropriate in the early universe if wound strings are heavy - wrapping long cycles - and diluted. | interpretation 0.38 | 0.18 | 0.03 | asserted 0.67 |
| s3 | We consider the dynamics of a string gas coupled to dilaton-gravity and find that a) for any number of dimensions the universe generically stays trapped in the Hagedorn regime and b) if the universe fluctuates to a radiation regime any residual winding modes are diluted enough so that they freeze-out in d > 3 large dimensions while they generically annihilate for d = 3. | result 0.99 | 0.94 | 0.61 | asserted 1.00 |
| s4 | In this sense the Brandenberger-Vafa mechanism is operative. | interpretation 1.00 | 0.61 | 0.52 | asserted 0.97 |
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The paper
Original abstract
We study string gas dynamics in the early universe and seek to realize the Brandenberger - Vafa mechanism - a goal that has eluded earlier works - that singles out three or fewer spatial dimensions as the number which grow large cosmologically. Considering wound string interactions in an impact parameter picture, we show that a strong exponential suppression in the interaction rates for d > 3 spatial dimensions reflects the classical argument that string worldsheets generically intersect in at most four spacetime dimensions. This description is appropriate in the early universe if wound strings are heavy - wrapping long cycles - and diluted. We consider the dynamics of a string gas coupled to dilaton-gravity and find that a) for any number of dimensions the universe generically stays trapped in the Hagedorn regime and b) if the universe fluctuates to a radiation regime any residual winding modes are diluted enough so that they freeze-out in d > 3 large dimensions while they generically annihilate for d = 3. In this sense the Brandenberger-Vafa mechanism is operative.
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References
How the literature uses it
11 arXiv papers cite this in 22 sentences
Papers citing it · 19 sentences without a confident label
Cites it as support 1 paper
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This argument was supported by numerical studies of string evolution in three and four spatial dimensions [ref] (see also [ref] ) [See [ref] for some caveats to this argument.].
Do we have a Theory of Early Universe Cosmology? · Emergent Universe · 0.98
Cites it as background 2 papers
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Several lines of research with different goals have emerged, among them are the stabilization of extra dimensions by massive, classical string gases [ref] or by quantum moduli trapping [ref] , isotropization of large dimensions [ref] , attempts to explain the late time acceleration in the visible dimensions via oscillations of the extra dimensions caused by competition of a stabilizing string gas and matter [ref] , dark matter candidates [ref] , attempts to explain the dimensionality of the observed large dimensions [ref] , bouncing/cyclic cosmologies caused by a coupling of a string gas with a modified gravity action [ref] , and an attempt to provide a non-inflationary explanation of the nearly scale invariant spectrum of scalar perturbations by means of thermal fluctuations during a quasi-static Hagedorn phase [ref] , which is assumed to be directly connected to an expanding, radiation
The Relic Problem of String Gas Cosmology · Introduction · 0.97
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For a sampling of publications, see [ref] , with more references to earlier work available in the reviews [ref] .
Microscopic approach to string gas cosmology · Introduction · 0.97
What it cites · 18 sentences without a confident label
Builds on 2 papers
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In a paper by Alexander, Brandenberger and Easson [ref] the setup of [ref] was extended to include p-branes for $p=0,1,2,4,5,6,8$ in the weak-coupling limit of M-theory with one small dimension compactified on $S^1$ (type IIA string theory).
Brane Gases in the Early Universe · Introduction · 0.99
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By removing the randomness in the choice of initial radii present in [ref] we can see more clearly the dependence of the winding annihilations on the number of growing dimensions.
String windings in the early universe · Equations of motion · 0.83
Uses the method or tool of 1 paper
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By way of outline we begin with a discussion of the impact parameter representation, proceed to set up our model for the string gas, and finish with a numerical simulation, along the lines of [ref] , that will allow us to identify the regions of phase space in which three or more spatial dimensions decompactify.
String windings in the early universe · Introduction · 0.97
Compares with 2 papers
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This is related to the limiting value of $λ(t)$ as $t→∞$ in the solution to the equations of motion ([ref]) in thermal equilibrium [ref] and it is also the same behaviour found in [ref] at exact equilibrium.
Aspects of String-Gas Cosmology at Finite Temperature · Results · 0.83
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This is related to the limiting value of $λ(t)$ as $t→∞$ in the solution to the equations of motion ([ref]) in thermal equilibrium [ref] and it is also the same behaviour found in [ref] at exact equilibrium.
Bouncing and cyclic string gas cosmologies · Results · 0.83
Cites as support 1 paper
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In [ref] , using numerical simulations for string networks on toroidal orbifolds with trivial fundamental group, the authors showed that pseudo-wound strings generically do persist for many Hubble times, suggesting that the requirement of non-contractible cycles can be relaxed.
Cosmological String Gas on Orbifolds · Introduction · 0.98
Cites as background 3 papers
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One of the few mechanisms aiming to explain the hierarchy between three large and six small spatial dimensions within superstring theory is due to a suggestion, some two decades ago, by Brandenberger and Vafa [ref] ; see [ref] for a review.
String Gas Cosmology · Introduction · 0.89
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For further details on the thermodynamic phases and energy conservation see [ref] and references therein.
String windings in the early universe · Equations of motion · 1.00
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For further details on the thermodynamic phases and energy conservation see [ref] and references therein.
Bouncing and cyclic string gas cosmologies · Equations of motion · 1.00
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