On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

Ambjørn, J.; Anagnostopoulos, Konstantinos N.; Bietenholz, Wolfgang; Hofheinz, Frank; Nishimura, Jun

doi:10.1103/physrevd.65.086001

Cited by 48 publications

(66 citation statements)

References 30 publications

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“…Eventually we would like to examine the possibility that our 4-dimensional space time appears dynamically in 10-dimensional string theory [5,6,7,8,9,10]. Monte Carlo simulation of the matrix model suffers from the complex action problem, and there are evidences that the imaginary part of the action plays a crucial role in the dynamical reduction of the space-time dimensionality [7].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

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

2002

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“…The Gaussian approximation up to the order 2 can not reproduce this non-analyticity, but the approximation is considered to get better in the 't Hooft limit from the observation that the non-analyticity vanishes in the 't Hooft limit [24]. S 0 ) C,0 are same as the ones obtained in the bosonic case [17] (eqs.…”

Section: Wilson Loopmentioning

confidence: 53%

Gaussian and mean field approximations for reduced 4D supersymmetric Yang-Mills integral

Sugino

2001

J. High Energy Phys.

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In this paper, we consider a reduced supersymmetric Yang-Mills integral with four supercharges by using a Gaussian approximation scheme and its improved version. We calculate the free energy and the expectation values of Polyakov loop and Wilson loop operators by extending the method employed in the bosonic case in the previous paper. Our results nicely match to the exact and the numerical results obtained before. The loop amplitudes exhibit good scaling behaviors similarly as in the bosonic case. The 't Hooft like large N limit leads simple formulas for the case of the loop length smaller. Also, the Polyakov loop and the Wilson loop are computed for the case of the loop length sufficiently large, where we see that the behavior of the Wilson loop reproduces the result simulated for a few smaller values of N at least qualitatively.

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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%

“…It has been recognized from those works that the fermionic part of the action plays a crucial role [5,6,7,8,9,10,11].…”

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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On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

Cited by 48 publications

References 30 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

Gaussian and mean field approximations for reduced 4D supersymmetric Yang-Mills integral

Improved perturbation method and its application to the IIB matrix model

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