Improved perturbation theory and four-dimensional space-time in IIB matrix model,” Prog

We have analyzed the IIB matrix model on the basis of the improved mean field approxi-mation (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 conver-gence of the improved series, that is, the appearance of a “plateau”. In this paper, we carry out higher-order calculations, and find that our improved free energy tends to have a plateau, which shows that IMFA works well in the IIB matrix model. §1. Introduction and summary String theory has been proposed as a unified theory of fundamental interactions including gravity. If it is the well-defined quantum gravity theory which our nature adopts, it should be able to predict several properties of our universe, for instance, the gauge symmetry at low energy, the particle content and their masses, and th