Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry

TL;DR

This paper uses the gaussian expansion method to analyze a simplified matrix model, demonstrating convergence and identifying spontaneous symmetry breaking patterns similar to those conjectured for the IIB matrix model, shedding light on space-time generation.

Contribution

The study applies the gaussian expansion method to a simplified matrix model, providing evidence of convergence and clarifying the symmetry breaking pattern.

Findings

Convergence of results up to 9th order.

Identification of symmetry breaking pattern.

Calculation of space-time extent in each direction.

Abstract

Recently the gaussian expansion method has been applied to investigate the dynamical generation of 4d space-time in the IIB matrix model, which is a conjectured nonperturbative definition of type IIB superstring theory in 10 dimensions. Evidence for such a phenomenon, which is associated with the spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up to the 7-th order calculations. Here we apply the same method to a simplified model, which is expected to exhibit an analogous spontaneous symmetry breaking via the same mechanism as conjectured for the IIB matrix model. The results up to the 9-th order demonstrate a clear convergence, which allows us to unambiguously identify the actual symmetry breaking pattern by comparing the free energy of possible vacua and to calculate the extent of ``space-time'' in each direction.