The emergence of expanding space-time in a novel large-$N$ limit of the Lorentzian type IIB matrix model

TL;DR

This paper introduces a modified Lorentzian type IIB matrix model with a mass term and demonstrates through complex Langevin simulations that an expanding Lorentzian space-time emerges in the large-$N$ limit, offering insights into non-perturbative superstring theory.

Contribution

It proposes a novel large-$N$ limit with a vanishing mass term coefficient that results in emergent expanding Lorentzian space-time, addressing previous issues with Euclidean space-time appearance.

Findings

Emergence of expanding Lorentzian space-time in the modified model

Use of complex Langevin simulations to handle the sign problem

The model provides a promising non-perturbative approach to superstring theory

Abstract

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. However, it was found recently that a Euclidean space-time appears in the conventional large-$N$ limit. In this work, we add a Lorentz invariant mass term to the original model and consider a limit, in which the coefficient of the mass term vanishes at large $N$. By performing complex Langevin simulations to overcome the sign problem, we observe the emergence of expanding space-time with the Lorentzian signature.