Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions

TL;DR

This paper investigates a Lorentzian matrix model for superstring theory in (9+1) dimensions, demonstrating that it can produce an expanding (3+1)-dimensional universe with SO(3) symmetry emerging dynamically.

Contribution

It introduces a regularization method for the Lorentzian matrix model and shows the spontaneous emergence of a (3+1)-dimensional expanding universe with SO(3) symmetry.

Findings

The model's infrared cutoffs can be removed in the large-N limit.

Three spatial dimensions begin to expand at a critical time.

The resulting universe exhibits SO(3) symmetry instead of SO(9).

Abstract

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous proposal in which the Wick rotation was used to make the model well-defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some "critical time", after which the space has SO(3) symmetry instead of SO(9).