Mean field approximation of IIB matrix model and emergence of four-dimensional space–time

Kawai, Hiroyuki; Kawamoto, Shoichi; Kuroki, Tsunehide; Matsuo, Tatsuhiro; Shinohara, Shun'ichi

doi:10.1016/s0550-3213(02)00908-2

Cited by 98 publications

(177 citation statements)

References 20 publications

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“…In that case, the symmetry breaking actually occurs, and it is shown to be a consequence of the fact that the action is complex. Also, the results in [80] give indications of a spontaneous symmetry breaking in the IKKT-model. However, the actual mechanism for having such a behaviour (if confirmed) remains an open question.…”

Section: Introductionmentioning

confidence: 81%

“…During the last few years it has been claimed that the "rotational" O(D) symmetry (where D is the number of matrices) might be spontaneously broken in the large N limit [76]. This issue has been analyzed in a series of analytical and numerical studies [69,70,71,72,73,74,77,78,79,80,81] and a possible mechanism for having such a spontaneous symmetry breaking has been proposed in [77,78,79].…”

Section: Introductionmentioning

confidence: 99%

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Rotational symmetry breaking in multimatrix models

Vernizzi

Wheater

2002

Phys. Rev. D

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We consider a class of multi-matrix models with an action which is O(D)-invariant, where D is the number of N × N Hermitian matrices X µ , µ = 1, . . . , D. The action is a function of all the elementary symmetric functions of the matrix T µν = T r(X µ X ν )/N . We address the issue whether the O(D) symmetry is spontaneously broken when the size N of the matrices goes to infinity. The phase diagram in the space of the parameters of the model reveals the existence of a critical boundary where the O(D) symmetry is maximally broken.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Rotational symmetry breaking in multimatrix models

Vernizzi

Wheater

2002

Phys. Rev. D

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“…This new aspect of symmetry should be explored further in the context of the general idea that spacetime and gravity are emergent phenomena [57][58][59][60][61][62][63][64][65][66][67][68] .…”

Section: Summary Discussion and Future Prospectsmentioning

confidence: 99%

Tensor models and 3-ary algebras

Sasakura¹

2011

Journal of Mathematical Physics

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Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.

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“…The Gaussian expansion method was reformulated as an improvement of perturbative series expansion in Ref. [27]. The improved Taylor expansion (ITE), as it is referred, opened a way toward more general applications that 1 A novel technique called the factorization method is proposed to resolve the complex action problem in the Monte Carlo simulations [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…The ITE prescription was employed for the IIB matrix model up to fifth order of perturbation in Ref. [27]. It has been proceeded to even higher orders and extended ansatz [28,29,30].…”

Section: Introductionmentioning

confidence: 99%

Improved perturbation method and its application to the IIB matrix model

Aoyama

Shibusa

2006

Nuclear Physics B

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We present a new scheme for extracting approximate values in "the improved perturbation method", which is a sort of resummation technique capable of evaluating a series outside the radius of convergence.We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the "plateau" structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively.We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.

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Mean field approximation of IIB matrix model and emergence of four-dimensional space–time

Cited by 98 publications

References 20 publications

Rotational symmetry breaking in multimatrix models

Rotational symmetry breaking in multimatrix models

Tensor models and 3-ary algebras

Improved perturbation method and its application to the IIB matrix model

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