IIB Matrix Model

Aoki, Hajime; Iso, Satoshi; Kawai, Hiroyuki; Kitazawa, Yoshihisa; Tsuchiya, Asato; Tada, Tsukasa

doi:10.1143/ptps.134.47

Cited by 168 publications

(350 citation statements)

References 9 publications

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“…In this model space-time is represented by A µ , and hence treated dynamically [5]. It is Euclidean as a result of the Wick rotation, which is always necessary in path integral formalisms.…”

Section: The Superstring Matrix Modelmentioning

confidence: 99%

New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

2002

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Monte Carlo simulations of a system whose action has an imaginary part are considered to be extremely difficult. We propose a new approach to this 'complex-action problem', which utilizes a factorization property of distribution functions. The basic idea is quite general, and it removes the so-called overlap problem completely. Here we apply the method to a nonperturbative study of superstring theory using its matrix formulation. In this particular example, the distribution function turns out to be positive definite, which allows us to reduce the problem even further. Our numerical results suggest an intuitive explanation for the dynamical generation of 4d space-time.

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Section: The Superstring Matrix Modelmentioning

confidence: 99%

New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

2002

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“…[15]). In particular, the notorious sign problem, which has been hindering Monte Carlo studies may have been recently reduced [16].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Yang-Mills Quantum Mechanics

Wosiek

2002

Confinement, Topology, and Other Non-Perturbative Aspects of QCD

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Abstract. The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a given system can then be automatically obtained. The method is applied to Wess-Zumino quantum mechanics and D=2 and D=4 supersymmetric Yang-Mills quantum mechanics with the SU(2) gauge group. Convergence with increasing size of the basis was observed in various cases. Many old results were confirmed and some new ones, especially for the D=4 system, are derived. Preliminary results in higher dimensions are also presented. In particular the spectrum of the zero-volume glueballs in 4 < D < 11 is obtained for the first time.

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“…We concentrate on the possibility of the spontaneous breakdown of Lorentz symmetry in the present article. We applied our scheme to the analysis of the improved series up to eighth order of perturbation for SO (4) and SO (7) ansatz that have been obtained in former works. As a result, we found a new solution that corresponds to the tendimensional universe besides the four-and seven-dimensional solutions already found previously.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore we are forced to pursue non-perturbative formulations. The IIB matrix model (also called the IKKT matrix model) is proposed as a constructive formulation of the superstring theory [3,4].…”

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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IIB Matrix Model

Cited by 168 publications

References 9 publications

New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

Supersymmetric Yang-Mills Quantum Mechanics

Improved perturbation method and its application to the IIB matrix model

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