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The type IIB matrix model is one of the most promising candidates for anonperturbative formulation of superstring theory. In particular, itsLorentzian version was shown to exhibit an interesting real-time dynamics suchas the spontaneous breaking of the 9-dimensional rotational symmetry to the3-dimensional one. This result, however, was obtained after regularizing theoriginal matrix integration by introducing "infrared" cutoffs on the quadraticmoments of the Hermitian matrices. In this paper, we generalize the form of thecutoffs in such a way that it involves an arbitrary power ($2p$) of thematrices. By performing Monte Carlo simulation of a simplified model, we findthat the results become independent of $p$ and hence universal for $p \gtrsim1.3$. For $p$ as large as 2.0, however, we find that large-$N$ scalingbehaviors do not show up, and we cannot take a sensible large-$N$ limit. Thuswe find that there is a certain range of $p$ in which a universal large-$N$limit can be taken. Within this range of $p$, the dynamical space-timedimensionality turns out to be $(3+1)$, while for $p=2.0$, where we cannot takea sensible large-$N$ limit, we observe a (5+1)d structure.

Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model