On the structure of the emergent 3D expanding space in the Lorentzian type {IIB} matrix model

The emergence of (3+1)D expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon that has been observed in Monte Carlo studies of this model. In particular, this may be taken as support for 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 eiSb by eβSb (β > 0) in the partition function, where Sb is the bosonic part of the action. We also discuss the possibility of obtaining a regular space-time with the (3+1)D expanding behavior in the original model with the correct eiSb factor.