Geometry in transition in four dimensions: A model of emergent geometry in the early universe

Ydri, Badis; Khaled, Ramda; Rouag, A.

doi:10.1103/physrevd.94.085020

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…The 6−dimensional IKKT Yang-Mills matrix models studied here present thus an appealing picture of a 4−dimensional geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early universe. See [42] and references therein.…”

Section: Resultsmentioning

confidence: 99%

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Emergent fuzzy geometry and fuzzy physics in four dimensions

2017

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A detailed Monte Carlo calculation of the phase diagram of bosonic IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are observed with a fluctuation given by a noncommutative U (1) gauge theory very weakly coupled to normal scalar fields. The geometry, which is determined dynamically, is given by the fuzzy spheres S 2 N and S 2 N ×S 2 N respectively. The three and six matrix models are in the same universality class with some differences. For example, in two dimensions the geometry is completely stable, whereas in four dimensions the geometry is stable only in the limit M −→ ∞, where M is the mass of the normal fluctuations. The behavior of the eigenvalue distribution in the two theories is also different. We also sketch how we can obtain a stable fuzzy foursphere S 2 N × S 2 N in the large N limit for all values of M as well as models of topology change in which the transition between spheres of different dimensions is observed. The stable fuzzy spheres in two and four dimensions act precisely as regulators which is the original goal of fuzzy geometry and fuzzy physics. Fuzzy physics and fuzzy field theory on these spaces are briefly discussed.

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Section: Resultsmentioning

confidence: 99%

“…Again the mass deformation parameter M is essentially the mass of these normal fluctuations and thus for large M these scalar fields become weakly coupled. In [42] an interpretation of these normal scalar fields as dark energy as dark energy is put forward.…”

Section: Introductionmentioning

confidence: 99%

Emergent fuzzy geometry and fuzzy physics in four dimensions

2017

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“…emergent geometry and topology change. 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 manymatrix model is what underlies the dynamical process of quantum geometry [64,65]. In summary, a new scenario for quantized geometry is proposed in this article.…”

Section: Discussionmentioning

confidence: 97%

Emergent geometry from random multitrace matrix models

2016

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A novel scenario for the emergence of geometry in random multitrace matrix models of a single hermitian matrix $M$ with unitary $U(N) $ invariance, i.e. without a kinetic term, is presented. In particular, the dimension of the emergent geometry is determined from the critical exponents of the disorder-to-uniform-ordered transition whereas the metric is determined from the Wigner semicircle law behavior of the eigenvalues distribution of the matrix $M$. If the uniform ordered phase is not sustained in the phase diagram then there is no emergent geometry in the multitrace matrix model.Comment: 18 pages, 7 figures (16 graphs), 1 tabl

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“…The original adjoint scalar fields X a of the U(N) gauge theory are seen to split into a genuine gauge field on the background geometry plus a bunch of massive normal scalar fields. See for example [49,50] and references therein. Furthermore, it is found that the background geometry is generically stable only in the region of the parameter space where the mass of these normal scalar fields is very large.…”

Section: Introductionmentioning

confidence: 99%

Quantum gravity as a multitrace matrix model

Ydri

Soudani

Rouag

2017

Int. J. Mod. Phys. A

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We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from two dimensions and captures a large class of spaces admiting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

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Geometry in transition in four dimensions: A model of emergent geometry in the early universe

Cited by 5 publications

References 31 publications

Emergent fuzzy geometry and fuzzy physics in four dimensions

Emergent fuzzy geometry and fuzzy physics in four dimensions

Emergent geometry from random multitrace matrix models

Quantum gravity as a multitrace matrix model

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