Progress in the numerical studies of the type IIB matrix model

TL;DR

This paper reviews recent numerical progress in studying the type IIB matrix model, highlighting developments in Euclidean and Lorentzian versions using advanced computational methods to understand space-time emergence.

Contribution

It provides a comprehensive overview of numerical techniques and results, including complex Langevin and Monte Carlo methods, clarifying their relationships and advancements in the field.

Findings

Recent results support space-time emergence from the model

Complex Langevin method overcomes sign problem in Lorentzian case

Comparison clarifies differences among various computational approaches

Abstract

The type IIB matrix model, also known as the IKKT model, has been proposed as a promising candidate for a non-perturbative formulation of superstring theory. Based on this proposal, various attempts have been made to explain how our four-dimensional space-time can emerge dynamically from superstring theory. In this article, we review the progress in numerical studies on the type IIB matrix model. We particularly focus on the most recent results for the Euclidean and Lorentzian versions, which are obtained using the complex Langevin method to overcome the sign problem. We also review the earlier results obtained using conventional Monte Carlo methods and clarify the relationship among different calculations.