The spontaneous breakdown of SO(10) symmetry of the IIB matrix model has been studied by using the improved mean field approximation (IMFA). In this report, the eighth-order contribution to the improved perturbative series is obtained, which involves evaluation of 20410 planar two-particle irreducible vacuum diagrams. We consider SO(d)-preserving configurations as ansatz (d = 4, 7). The development of plateau, the solution of self-consistency condition, is seen in both ansatz. The large ratio of the space-time extent of d-dimensional part against the remaining (10 − d)-dimensional part is obtained for SO(4) ansatz evaluated at the representative points of the plateau. It would be interpreted as the emergence of four-dimensional space-time in the IIB matrix model.

We investigate the origin of our four-dimensional space-time by considering dynamical aspects of the IIB matrix model using the improved mean field approximation. Previous works have focused on the specific choices of configurations as ansatz which preserve SO(d) rotational symmetry. In this report, an extended ansatz is proposed and examined up to a third-order approximation which includes both the SO(4) ansatz and the SO(7) ansatz in their respective limits. From the solutions of the self-consistency condition represented by the extrema of the free energy of the system, it is found that some of the solutions found in the SO(4) or SO(7) ansatz disappear in the extended ansatz. This implies that the extension of ansatz can be used to distinguish stable solutions from unstable solutions. It is also found that there is a non-trivial accumulation of extrema including the SO(4)-preserving solution, which may lead to the formation of a plateau.

We apply an improved Taylor expansion method, which is a variational scheme to the Ising model in two dimensions. This method enables us to evaluate the free energy and magnetization in strong coupling regions from the weak coupling expansion, even in the case of a phase transition. We determine the approximate value of the transition point using this scheme. In the presence of an external magnetic field, we find both stable and metastable physical states. * ) In Ref. 13) there appears a treatment of the application of the improved Taylor expansion method to the Ising model. Our arguments here extend and clarify the work given there. * ) One attempt to apply this method to non-abelian Yang-Mills theory can be found in Ref. 14).

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.

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.

We are developing an object oriented code set "Bridge++" for simulation of lattice gauge theories. It aims to be an extensible, readable, and portable workbench while keeping sufficiently high performance in actual productive runs. This paper describes the status of two extensions. One is multi-threading with OpenMP in the recently released version 1.2. The other is a design to use arithmetic accelerator devices such as GPGPUs, which is still under developing version. Feasibility test is performed with OpenCL.

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This article reports our project on the automated calculation of QED corrections to the anomalous magnetic moment of leptons. Our major concern is the tenth-order correction, which is urgently needed considering the recent improvement of electron g−2 measurements. We focus on a type of diagrams that have no internal lepton loops, and have devised the automated code-generating system for the UV-renormalized amplitude. We have newly developed and implemented an efficient algorithm to perform subtractions of IR divergences. This enables us to obtain finite amplitudes that are free from both UV and IR divergences. Currently the numerical evaluation of these diagrams of tenth order is in progress.