Abstract:We have analyzed the IIB matrix model on the basis of the improved mean field approximation (IMFA) and have obtained evidence suggesting that the four-dimensional space-time appears as its most stable vacuum. This method is a systematic way to obtain an improved perturbation series and was first applied to the IIB matrix model by Nishimura and Sugino. In a previous paper, we reformulated this method and proposed a criterion for the convergence of the improved series, that is, the appearance of a "plateau". In … Show more
“…The mechanism that realizes the brane world in this way has been studied in Refs. [4,5], and by now there are certain evidences that indeed four-dimensional space-time is generated dynamically [6][7][8][9].…”
It has been known that the dynamics of k coincident D-branes in string theory is described effectively by U(k) Yang-Mills theory at low energy. While these configurations appear as classical solutions in matrix models, it was not clear whether it is possible to realize the k = 1 case as the true vacuum. The massive Yang-Mills-Chern-Simons matrix model has classical solutions corresponding to all the representations of the SU(2) algebra, and provides an opportunity to address the above issue on a firm ground. We investigate the phase structure of the model, and find in particular that there exists a parameter region where O(N ) copies of the spin-1/2 representation appear as the true vacuum, thus realizing a nontrivial gauge group dynamically. Such configurations are analogous to the ones that are interpreted in the BMN matrix model as coinciding transverse 5-branes in M-theory.
“…The mechanism that realizes the brane world in this way has been studied in Refs. [4,5], and by now there are certain evidences that indeed four-dimensional space-time is generated dynamically [6][7][8][9].…”
It has been known that the dynamics of k coincident D-branes in string theory is described effectively by U(k) Yang-Mills theory at low energy. While these configurations appear as classical solutions in matrix models, it was not clear whether it is possible to realize the k = 1 case as the true vacuum. The massive Yang-Mills-Chern-Simons matrix model has classical solutions corresponding to all the representations of the SU(2) algebra, and provides an opportunity to address the above issue on a firm ground. We investigate the phase structure of the model, and find in particular that there exists a parameter region where O(N ) copies of the spin-1/2 representation appear as the true vacuum, thus realizing a nontrivial gauge group dynamically. Such configurations are analogous to the ones that are interpreted in the BMN matrix model as coinciding transverse 5-branes in M-theory.
“…Although we do not yet have a rigorous definition of plateaux, we could identify them by their properties investigated in [9,13,19,20] as follows. The ideal realization of the plateau may have such a property that the improved series is totally independent of the artificial parameters ξ 0 in a certain region.…”
Section: The Improved Perturbation Theorymentioning
confidence: 99%
“…[10,11], which has been further investigated in various manners [12,13,14]. This technique is a sort of variational method [15] to extract nonperturbative information on the vacuum of a theory.…”
Section: Introductionmentioning
confidence: 99%
“…The IMFA has been applied successfully to a number of models to yield nonperturbative results [9,10,11,12,13,14,16,17,18,19,20]. In particular, the IMFA was applied to the IIB matrix model first in Ref.…”
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It also gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua.
“…[27]. It has been proceeded to even higher orders and extended ansatz [28,29,30]. The mechanism of the spontaneous symmetry breakdown is further examined in a simplified model via the Gaussian expansion method in Ref.…”
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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