Quantum gravity as a multitrace matrix model

Ydri, Badis; Soudani, Cherine; Rouag, A.

doi:10.1142/s0217751x17501809

Cited by 4 publications

(3 citation statements)

References 88 publications

(96 reference statements)

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“…It has been shown in [60,61] that the essential features of the phase diagram of noncommutative phi-four theory in two dimensions can be captured by a truncated multitrace matrix model depending on the cubic moment TrM 3 , i.e. a multitrace matrix model given simply by the potential…”

Section: The Multitrace Matrix Model and The Saddle Point Equationmentioning

confidence: 99%

“…See figure (1). This idea and its generalization to more general multitrace matrix models and other noncommutative spaces is the underpinning of the proposal of emergent geometry from random multitrace matrix models which was originally laid down in [60][61][62][63] using different methods (renormalization group equation, Monte Carlo algorithm and large N saddle point method).…”

Section: The Multitrace Matrix Model and The Saddle Point Equationmentioning

confidence: 99%

“…In summary, our proposal for "emergent geometry from random multitrace matrix models" consists of five ingredients [60][61][62][63]:…”

Section: Emergent Geometry As Emergence Of the Uniform-ordermentioning

confidence: 99%

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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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Section: The Multitrace Matrix Model and The Saddle Point Equationmentioning

confidence: 99%

Section: The Multitrace Matrix Model and The Saddle Point Equationmentioning

confidence: 99%

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Emergent geometry from random multitrace matrix models

2016

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On Random Multitraces Matrix Models

Khaled

2022

Int J Theor Phys

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Quantized noncommutative geometry from multitrace matrix models

Ydri

Khaled²,

Soudani

2022

Int. J. Mod. Phys. A

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In this paper, the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is proposed in which noncommutative geometry can emerge from “one-matrix multitrace scalar matrix models” by probing the statistical physics of commutative phases of matter. This is in contrast to the usual mechanism in which noncommutative geometry emerges from “many-matrix singletrace Yang–Mills matrix models” by probing the statistical physics of noncommutative phases of gauge theory. In this novel scenario, quantized geometry emerges in the form of a transition between the two phase diagrams of the real quartic matrix model and the noncommutative scalar phi-four field theory. More precisely, emergence of the geometry is identified here with the emergence of the uniform-ordered phase and the corresponding commutative (Ising) and noncommutative (stripe) coexistence lines. The critical exponents and Wigner’s semicircle law are used to determine the dimension and the metric, respectively. Arguments from the saddle point equation, from Monte Carlo simulation and from the matrix renormalization group equation are provided in support of this scenario.

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Quantum gravity as a multitrace matrix model

Cited by 4 publications

References 88 publications

Emergent geometry from random multitrace matrix models

Emergent geometry from random multitrace matrix models

On Random Multitraces Matrix Models

Quantized noncommutative geometry from multitrace matrix models

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