Dynamical aspects of large-N reduced models

Hotta, T.; Nishimura, Jun; Tsuchiya, Asato

doi:10.1016/s0550-3213(99)00056-5

Cited by 135 publications

(307 citation statements)

References 18 publications

(46 reference statements)

Supporting

Mentioning

278

Contrasting

Order By: Relevance

“…The results can be fitted to C 6 + C 7 N −2 as one can see from figure 3. This large-N behavior is analogous to the one observed in the bosonic IKKT model [24]. Thus we can obtain the final result for the matrix QM (2.1).…”

Section: Monte Carlo Simulationsupporting

confidence: 80%

“…JHEP09 (2005) Monte Carlo simulation of the models (3.1) and (2.2) can be performed by the heat bath algorithm [24]. For the cQEK model, we first take an average over the ensemble {X i } with the action (2.2) for each Ω, and then perform the averaging over Ω by using random numbers distributed uniformly within the region [− Λ 2 , Λ 2 ].…”

Section: Monte Carlo Simulationmentioning

confidence: 99%

“…In the bosonic IKKT model it is known that the SO(d) symmetry is not spontaneously broken and 1 N tr(A µ ) 2 bIKKT ∼ O(1) [24], which implies that the extent of the eigenvalue distribution is of O (1) …”

Section: Relation To the Bosonic Ikkt Modelmentioning

confidence: 99%

See 2 more Smart Citations

The large-Nreduction in matrix quantum mechanics — a bridge between BFSS and IKKT —

Kawahara

Nishimura

2005

J. High Energy Phys.

Self Cite

View full text Add to dashboard Cite

The large N reduction is an equivalence between large N gauge theories and matrix models discovered by Eguchi and Kawai in the early 80s. In particular the continuum version of the quenched Eguchi-Kawai model may be useful in studying supersymmetric and/or chiral gauge theories nonperturbatively. We apply this idea to matrix quantum mechanics, which is relevant, for instance, to nonperturbative studies of the BFSS Matrix Theory, a conjectured nonperturbative definition of M-theory. In the bosonic case we present Monte Carlo results confirming the equivalence directly, and discuss a possible explanation based on the Schwinger-Dyson equations. In the supersymmetric case we argue that the equivalence holds as well although some care should be taken if the rotational symmetry is spontaneously broken. This equivalence provides an explicit relation between the BFSS model and the IKKT model, which may be used to translate results in one model to the other.

show abstract

Section: Monte Carlo Simulationsupporting

confidence: 80%

Section: Monte Carlo Simulationmentioning

confidence: 99%

See 1 more Smart Citation

The large-Nreduction in matrix quantum mechanics — a bridge between BFSS and IKKT —

Kawahara

Nishimura

2005

J. High Energy Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…results with those for the corresponding bosonic theory [11], revealed that supersymmetry indeed plays an important role in the dynamics of large-N reduced models as a nonperturbative definition of string theories. Unfortunately, such a direct approach does not work in the IIB matrix model as it stands, due to the fact that the effective action induced by fermions is generically complex, whereas in the above mentioned four-dimensional version, it is real.…”

mentioning

confidence: 80%

Spontaneous breakdown of Lorentz invariance in IIB matrix model

Nishimura¹,

Vernizzi²

2000

J. High Energy Phys.

Self Cite

153

View full text Add to dashboard Cite

We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter ν which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary ν, and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at ν = ∞ using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue that it is likely that the remaining eight-dimensional Lorentz invariance is further broken, which can be checked by integrating over the saddle-point configurations using standard Monte Carlo simulation.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Dynamical aspects of large-N reduced models

Cited by 135 publications

References 18 publications

The large-Nreduction in matrix quantum mechanics — a bridge between BFSS and IKKT —

The large-Nreduction in matrix quantum mechanics — a bridge between BFSS and IKKT —

Spontaneous breakdown of Lorentz invariance in IIB matrix model

Improved perturbation method and its application to the IIB matrix model

Contact Info

Product

Resources

About