Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

TL;DR

This paper demonstrates analytically that four-dimensional space-time can emerge dynamically from the IIB matrix model, supporting the idea that our universe's four-dimensional structure arises from fundamental string theory principles.

Contribution

It introduces a Gaussian expansion approach with higher order corrections to analyze symmetry breaking in the IIB matrix model, providing evidence for four-dimensional space-time emergence.

Findings

SO(4) symmetry breaking solution has the lowest free energy.

The space-time extent in four directions exceeds that in six.

Results align with previous analytic formulas as order increases.

Abstract

We study the spontaneous breakdown of SO(10) symmetry in the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory in ten dimensions. Our analysis is based on a Gaussian expansion technique, which was originally proposed by Kabat-Lifschytz and applied successfully to the strong coupling dynamics of the Matrix Theory. We propose a prescription for including higher order corrections, which yields a rapid convergence in a simple example. This prescription is then applied to the IIB matrix model up to the third order. We find that the `self-consistency equations' allow various symmetry breaking solutions. Among them, the solution preserving SO(4) symmetry is found to have the smallest free energy. The value of the free energy comes closer to the analytic formula obtained by Krauth-Nicolai-Staudacher as we increase the order. The extent of the space-time in the 4 directions is larger than the remaining 6 directions, and the ratio increases with the order. These results provide the first analytical evidence that four-dimensional space-time is generated dynamically in the IIB matrix model.