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

TL;DR

This paper investigates the spontaneous emergence of four-dimensional space-time in the IIB matrix model by calculating higher-order terms in the improved mean field approximation, revealing a large space-time ratio consistent with four-dimensionality.

Contribution

It provides the eighth-order contribution to the improved perturbative series and demonstrates the emergence of four-dimensional space-time within the IIB matrix model.

Findings

Large ratio of 4D space-time extent observed

Development of plateau in self-consistency solutions

Evidence supporting emergence of 4D 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.