H[atakeyama]{}$^{1,2)}$, Akira M[atsumoto]{}$^{3)}$, Jun N[ishimura]{}$^{3,4)}$,\
Asato T[suchiya]{}$^{1,2)}$ Atis Y[osprakob]{}$^{3)}$\

$^{1)}$ [*Department of Physics, Shizuoka University*]{}\
[*836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan*]{}\
$^{2)}$ [*Graduate School of Science and Technology, Shizuoka University*]{}\
[*3-5-1 Johoku, Naka-ku, Hamamatsu 432-8011, Japan*]{}\
$^{3)}$ [*Department of Particle and Nuclear Physics, School of High Energy Accelerator Science,*]{}\
[*Graduate University for Advanced Studies (SOKENDAI)*]{}\
[*1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan*]{}\
$^{4)}$ [*KEK Theory center, High Energy Accelerator Organization*]{}\
[*1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan*]{}

Introduction
============

Superstring theory has been investigated intensively as a unified theory including quantum gravity. However, in its perturbative formulation that has been established so far, there exist tremendously many stable vacua corresponding to various space-time dimensionality, gauge group and matter contents. Also it is known that the cosmic singularity at the beginning of the Universe cannot be resolved within perturbative superstring theory [@Lawrence:2002aj; @Liu:2002kb; @Horowitz:2002mw; @Berkooz:2002je]. In order to address these issues, nonperturbative formulation is clearly needed, and the matrix models [@Banks:1996vh; @Ishibashi:1996xs; @Dijkgraaf:1997vv] have been proposed as its candidates.

In this paper, we focus on the type IIB matrix model [@Ishibashi:1996xs], which is distinctive in that not only space but also time emerges dynamically from the matrix degrees of freedom. Indeed it was 