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Geometry in transition in four dimensions: A model of emergent geometry in the early universe and dark energy
High Energy Physics - Theory · Submitted 22 Jul 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field which is very weakly coupled to two normal scalar fields playing the role of dark energy.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field which is very weakly coupled to two normal scalar fields playing the role of dark energy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. | contribution 0.56 | 0.76 | 0.03 | asserted 0.96 |
| s1 | This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. | result 0.99 | 0.84 | 0.33 | asserted 1.00 |
| s2 | This is an exotic phase transition in the same universality class as the three matrix model but with important differences. | interpretation 0.61 | 0.61 | 0.08 | asserted 1.00 |
| s3 | The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field which is very weakly coupled to two normal scalar fields playing the role of dark energy. | result 0.96 | 0.86 | 0.64 | asserted 1.00 |
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The paper
Original abstract
We study a six matrix model with global $SO(3)\times SO(3)$ symmetry containing at most quartic powers of the matrices. This theory exhibits a phase transition from a geometrical phase at low temperature to a Yang-Mills matrix phase with no background geometrical structure at high temperature. This is an exotic phase transition in the same universality class as the three matrix model but with important differences. The geometrical phase is determined dynamically, as the system cools, and is given by a fuzzy four-sphere background ${\bf S}^2_N\times{\bf S}^2_N$, with an Abelian gauge field which is very weakly coupled to two normal scalar fields playing the role of dark energy.
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How the literature uses it
4 arXiv papers cite this in 5 sentences
Papers citing it · 2 sentences without a confident label
Compares with it 1 paper
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This should be contrasted with the scenario of "emergent geometry through Yang-Mills matrix models" in which the structure and symmetry of the various singletrace terms of the many-matrix model is what underlies the dynamical process of quantum geometry [ref] .
Quantized Noncommutative Geometry from Multitrace Matrix Models · Conclusion · 0.99
Cites it as background 2 papers
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In [ref] an interpretation of these normal scalar fields as dark energy as dark energy is put forward.
Emergent fuzzy geometry and fuzzy physics in $4$ dimensions · Introduction · 0.82
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For recent work on fuzzy physics in $2$ and $4$ dimensions see [ref] .
Review of M(atrix)-Theory, Type IIB Matrix Model and Matrix String Theory · Co-adjoint orbits · 0.91
What it cites · 1 sentence without a confident label
Cites as background 1 paper
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See for example [ref] for an inspiring discussion, along the lines of causal sets and lattice dynamical triangulation respectively, and [ref] for some other recent ideas from strings and random matrix theory.
Emergent Spacetime · Introduction · 0.98
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