# Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model

## TL;DR

This study applies the complex Langevin method to the Lorentzian type IIB matrix model to address the sign problem, revealing a non-singular space-time structure while maintaining the emergent (3+1)D expansion.

## Contribution

It demonstrates that the complex Langevin method can overcome the sign problem in this model, leading to more realistic matrix configurations without the singular Pauli-matrix structure.

## Key findings

- Departure from Pauli-matrix structure in configurations
- Emergence of (3+1)D expanding space-time preserved
- Sign problem effectively mitigated using complex Langevin method

## Abstract

The Lorentzian type IIB matrix model has been studied as a promising candidate for a nonperturbative formulation of superstring theory. In particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. It has been found recently, however, that the matrix configurations generated by the simulation is singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem has been attributed to the approximation used to avoid the sign problem in simulating the model. Here we investigate the model using the complex Langevin method to overcome the sign problem instead of using the approximation. Our results indicate a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior is kept intact.