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


Abstract in English

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.

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