Improved Perturbation Theory and Four-Dimensional Space-Time in the IIB Matrix Model

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 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.