# A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

## TL;DR

This paper introduces a novel simulation method for analyzing late-time dynamics in the Lorentzian type IIB matrix model, enabling efficient study of large matrices and confirming the spontaneous symmetry breaking from 9D to 3D.

## Contribution

The paper develops a new effective theory-based simulation technique that reduces computational complexity for large matrices in the Lorentzian type IIB matrix model.

## Key findings

- Validated the new simulation method against simplified models.
- Confirmed spontaneous symmetry breaking from 9D to 3D.
- Demonstrated efficiency in handling matrices of size O(√N).

## Abstract

The type IIB matrix model has been investigated as a possible nonperturbative formulation of superstring theory. In particular, it was found by Monte Carlo simulation of the Lorentzian version that the 9-dimensional rotational symmetry of the spatial matrices is broken spontaneously to the 3-dimensional one after some "critical time". In this paper we develop a new simulation method based on the effective theory for the submatrices corresponding to the late time. Using this method, one can obtain the results for $N\times N$ matrices by simulating matrices typically of the size $O(\sqrt{N})$. We confirm the validity of this method and demonstrate its usefulness in simplified models.