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

Sugino, Fumihiko

doi:10.1088/1126-6708/2001/07/014

Cited by 22 publications

(13 citation statements)

References 24 publications

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“…[10,11]. Such a method for general supersymmetric models was originally proposed by with the particular intention of studying the strong-coupling regime of the Matrix Theory [13].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

Nishimura

Sugino

2002

J. High Energy Phys.

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127

215

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We study the spontaneous breakdown of SO(10) symmetry in the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory in ten dimensions. Our analysis is based on a gaussian expansion technique, which was originally proposed by Kabat-Lifschytz and applied successfully to the strong coupling dynamics of the Matrix Theory. We propose a prescription for including higher order corrections, which yields a rapid convergence in a simple example. This prescription is then applied to the IIB matrix model up to the third order. We find that the 'self-consistency equations' allow various symmetry breaking solutions. Among them, the solution preserving SO(4) symmetry is found to have the smallest free energy. The value of the free energy comes closer to the analytic formula obtained by Krauth-Nicolai-Staudacher as we increase the order. The extent of the space-time in the 4 directions is larger than the remaining 6 directions, and the ratio increases with the order. These results provide the first analytical evidence that four-dimensional space-time is generated dynamically in the IIB matrix model.

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“…[10,11]. Such a method for general supersymmetric models was originally proposed by with the particular intention of studying the strong-coupling regime of the Matrix Theory [13].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

Nishimura

Sugino

2002

J. High Energy Phys.

Self Cite

127

215

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“…We use here the first derivatives (25) and the second derivatives (26) in particular. Finally, we identify the region as plateau in which two distributions overlap with each other.…”

Section: Results In So(4) Ansatzmentioning

confidence: 99%

“…In the following investigation into the IIB matrix model, we use the two weight functions w 1 (25) and w 2 (26).…”

Section: Weighted Histogram Analysismentioning

confidence: 99%

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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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“…Precisely speaking, OPT is always applicable even if an action has no natural expansion parameters like supersymmetric Yang-Mills integral or IIB matrix model[14][15][16].…”

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confidence: 99%

Distribution of solutions of the fastest apparent convergence condition in optimized perturbation theory and its relation to anti-Stokes lines

Tsutsui

Doi

2019

Annals of Physics

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We discuss fundamental properties of the fastest apparent convergence (FAC) condition which is used as a variational criterion in optimized perturbation theory (OPT). We examine an integral representation of the FAC condition and a distribution of the zeros of the integral in a complex artificial parameter space on the basis of theory of Lefschetz thimbles. We find that the zeros accumulate on a certain line segment so-called anti-Stokes line in the limit K → ∞, where K is a truncation order of a perturbation series. This phenomenon gives an underlying mechanism that physical quantities calculated by OPT can be insensitive to the choice of the artificial parameter. * stsutsui@post.kek.jp 1 arXiv:1901.04353v1 [hep-th]

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

Cited by 22 publications

References 24 publications

Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

Improved perturbation method and its application to the IIB matrix model

Distribution of solutions of the fastest apparent convergence condition in optimized perturbation theory and its relation to anti-Stokes lines

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