# On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model

## TL;DR

This paper investigates the structure of emergent 3D expanding space in the Lorentzian type IIB matrix model, revealing that the expansion is linked to Pauli matrices and discussing implications of simulation approximations.

## Contribution

It analyzes the space-time structure in the Lorentzian type IIB matrix model and its simplified versions, highlighting the impact of simulation approximations on the emergent geometry.

## Key findings

- Expanding space is described by Pauli matrices in the simplified models.
- Simulation approximation replaces $e^{iS_b}$ with $e^{eta S_b}$, affecting results.
- Discussion on how to recover the original model's space-time structure.

## Abstract

The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplified versions, and find that the expanding part of the space is described essentially by the Pauli matrices. We argue that this is due to an approximation used in the simulation to avoid the sign problem, which actually amounts to replacing $e^{iS_{\rm b}}$ by $e^{\beta S_{\rm b}}$ ($\beta>0$) in the partition function, where $S_{\rm b}$ is the bosonic part of the action. We also discuss the possibility of obtaining a regular space-time with the (3+1)-dimensional expanding behavior in the original model with the correct $e^{iS_{\rm b}}$ factor.