Impact of supersymmetry on the dynamical emergence of the spacetime in the type IIB matrix model with the Lorentz symmetry "gauge fixed"

TL;DR

This paper explores how supersymmetry influences the spontaneous emergence of spacetime dimensions in the type IIB matrix model, employing advanced numerical methods to overcome computational challenges.

Contribution

It introduces a nonperturbative Lorentz gauge fixing and applies the Complex Langevin Method to study supersymmetry's role in spacetime emergence.

Findings

Supersymmetry affects the dynamical generation of spacetime dimensions.

The Complex Langevin Method effectively addresses the sign problem in simulations.

Lorentz symmetry fixing reduces numerical artifacts in the model.

Abstract

The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as the emergence of time and an expanding 3--dimensional space, they are hindered by the sign problem. We address this using the Complex Langevin Method (CLM). Furthermore, to suppress spurious numerical artifacts that originate from large Lorentz boosts due to the Lorentz symmetry of the model, we nonperturbatively fix the Lorentz symmetry using the Faddeev--Popov procedure. We then study this model to investigate the impact of supersymmetry on the dynamical generation of (3+1)--dimensional spacetime.