Relationship between the Euclidean and Lorentzian versions of the type IIB matrix model

TL;DR

This paper investigates the connection between Euclidean and Lorentzian versions of the type IIB matrix model, using complex Langevin simulations to explore how spacetime signature evolves dynamically over time.

Contribution

It introduces a constrained model that demonstrates the transition from Euclidean to Lorentzian spacetime signatures within the type IIB matrix model.

Findings

Spacetime metric transitions from Euclidean to Lorentzian over time.

Application of complex Langevin method overcomes sign problem in simulations.

Clarification of the relationship between Euclidean and Lorentzian models.

Abstract

The type IIB matrix model was proposed as a non-perturbative formulation of superstring theory in 1996. We simulate a model that describes the late time behavior of the IIB matrix model by applying the complex Langevin method to overcome the sign problem. We clarify the relationship between the Euclidean and the Lorentzian versions of the type IIB matrix model in a recently discovered phase. By introducing a constraint, we obtain a model where the spacetime metric is Euclidean at early times, whereas it {\it dynamically} becomes Lorentzian at late times.