Stability of 4-dimensional Space-time from IIB Matrix Model via Improved Mean Field Approximation

TL;DR

This study investigates the stability of four-dimensional space-time within the IIB matrix model using an improved mean field approximation, extending previous ansatz to identify stable solutions and potential formation of a plateau.

Contribution

An extended ansatz is proposed and analyzed up to third order, helping to distinguish stable solutions and understand the emergence of four-dimensional space-time.

Findings

Some solutions disappear with the extended ansatz, indicating stability filtering.

Accumulation of extrema suggests possible plateau formation.

Extended ansatz enhances understanding of space-time dimensionality emergence.

Abstract

The origin of our four-dimensional space-time has been pursued through the dynamical aspects of the IIB matrix model via the improved mean field approximation. Former works have been focused on the specific choice of configurations as ansatz which preserve SO(d) rotational symmetry. In this report, an extended ansatz is proposed and examined up to 3rd order of approximation which includes both SO(4) ansatz and SO(7) ansatz in their respective limits. From the solutions of self-consistency condition represented by the extrema of free energy of the system, it is found that a part of solutions found in SO(4) or SO(7) ansatz disappear in the extended ansatz. It implies that the extension of ansatz works as a device to distinguish the stable solutions from the unstable ones. It is also found that there is a non-trivial accumulation of extrema including the SO(4)-preserving solution, which may lead to the formation of plateau.