Matrix model cosmology in two space-time dimensions

Stern, A.

doi:10.1103/physrevd.90.124056

Cited by 21 publications

(39 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(See Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] for related works.) It was also suggested from Monte Carlo simulation of simplified models that the expansion is exponential at the beginning and it turns into a power law at late times [5,6].…”

Section: Introductionmentioning

confidence: 99%

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

Azuma

Ito

Nishimura

et al. 2017

Progress of Theoretical and Experimental Physics

View full text Add to dashboard Cite

The type IIB matrix model has been investigated as a possible nonperturbative formulation of superstring theory. In particular, it was found by Monte Carlo simulation of the Lorentzian version that the 9-dimensional rotational symmetry of the spatial matrices is broken spontaneously to the 3-dimensional one after some "critical time". In this paper we develop a new simulation method based on the effective theory for the submatrices corresponding to the late time. Using this method, one can obtain the results for N × N matrices by simulating matrices typically of the size O( √ N ). We confirm the validity of this method and demonstrate its usefulness in simplified models.

show abstract

Section: Introductionmentioning

confidence: 99%

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

Azuma

Ito

Nishimura

et al. 2017

Progress of Theoretical and Experimental Physics

View full text Add to dashboard Cite

show abstract

“…The lines are fits toR 2 (t) /R 2 (t c ) = a + (1 − a) exp (bx).The values of the fitting parameters a and b obtained by the fits are also presented in table 1. (Bottom) Zoom up of the plot at the top 16. 10 -0.68014(7) 0.04099(04) 0.983(03) 3.56(11) 1.1 256 16 6 -0.39307(6) 0.03213(14) 0.961(18) 5.36(39) 1.2 256 16 6 -0.34441(6) 0.02904(16) 0.976(12) 6.82(53) 1.3 256 16 6 -0.29213(8) 0.03055(11) 0.940(12) 8.10(28) 1.4 256 16 6 -0.23933(8) 0.02940(19) 0.944(27) 8.07(63) 1.5 256 16 6 -0.23593(7) 0.02579(02) 0.950(11) 8.24(30)…”

mentioning

confidence: 99%

Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model

Ito

Nishimura

Tsuchiya

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing "infrared" cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power (2p) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of p and hence universal for p 1.3. For p as large as 2.0, however, we find that large-N scaling behaviors do not show up, and we cannot take a sensible large-N limit. Thus we find that there is a certain range of p in which a universal large-N limit can be taken. Within this range of p, the dynamical space-time dimensionality turns out to be (3 + 1), while for p = 2.0, where we cannot take a sensible large-N limit, we observe a (5+1)d structure.

show abstract

“…, (D − 1) cover just half of de Sitter space. [25] Transformation from (12) to (13) can be understood if we restrict discussion on the two-dimensional κ-Minkowski space for which any right invariant metric with Lorentzian signature, up to an irrelevant scale, can be written in the form…”

Section: Classical Geometry Of the Lie Group Generated By The Lie Algmentioning

confidence: 99%

“…Whenever derivatives span a Lie algebra, the matrix algebra can be viewed as a quantization of the algebra of functions on a certain homogeneous space. Then, in principle, a quantization map can be defined explicitly, which might be particularly beneficial in an attempt to formulate quantized/non‐commutative counterparts of models used in cosmology or field theory on a curved background . Therefore, understanding of the quantization map associated to the κ‐Minkowski space in terms of matrix geometry is welcome.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy de Sitter Space from kappa‐Minkowski Space in Matrix Basis

Jurman

2019

Fortschritte der Physik

View full text Add to dashboard Cite

We consider the Lie group RκD generated by the Lie algebra of κ‐Minkowski space. Imposing the invariance of the metric under the pull‐back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with RκD. This metric coincides with the metric of de Sitter space‐time. We analyze the structure of unitary representations of the group RκD relevant for the realization of the non‐commutative κ‐Minkowski space by embedding into (2D−1)‐dimensional Heisenberg algebra. Using a suitable set of generalized coherent states, we select the particular Hilbert space and realize the non‐commutative κ‐Minkowski space as an algebra of the Hilbert‐Schmidt operators. We define dequantization map and fuzzy variant of the Laplace‐Beltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the Laplace‐Beltrami operator on the half of de Sitter space‐time.

show abstract

Matrix model cosmology in two space-time dimensions

Cited by 21 publications

References 42 publications

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model

Fuzzy de Sitter Space from kappa‐Minkowski Space in Matrix Basis

Contact Info

Product

Resources

About