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

## TL;DR

This study investigates the Lorentzian type IIB matrix model, revealing a universal 3+1 dimensional space-time structure in a certain cutoff range, with results independent of cutoff specifics, but showing different behavior at larger cutoff powers.

## Contribution

It introduces a generalized cutoff approach in the Lorentzian type IIB matrix model and demonstrates the universality of the resulting space-time dimensionality within a specific parameter range.

## Key findings

- Results are independent of cutoff power p for p ≥ 1.3.
- A universal 3+1 dimensional space-time emerges within a certain p range.
- At p=2.0, the model shows a 5+1 dimensional structure without a sensible large-N limit.

## Abstract

The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing "infrared" cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power ($2p$) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of $p$ and hence universal for $p \gtrsim 1.3$. For $p$ as large as 2.0, however, we find that large-$N$ scaling behaviors do not show up, and we cannot take a sensible large-$N$ limit. Thus we 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-time dimensionality turns out to be $(3+1)$, while for $p=2.0$, where we cannot take a sensible large-$N$ limit, we observe a (5+1)d structure.