Higher Order Terms of Improved Mean Field Approximation for IIB Matrix Model and Emergence of Four-dimensional Space-time

Abstract

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.