Monte Carlo Studies of the IIB Matrix Model at Large N

TL;DR

This study uses Monte Carlo simulations on a simplified bosonic version of the IIB matrix model to explore spontaneous Lorentz invariance breaking, revealing isotropy at large N and highlighting the importance of the imaginary part of the action.

Contribution

It explicitly formulates the effective theory of the IIB matrix model with bosonic variables and investigates Lorentz symmetry breaking through large N simulations.

Findings

Eigenvalue distribution follows power-law behavior with N

Distribution becomes more isotropic as N increases

Imaginary part of the action may be crucial for Lorentz symmetry breaking

Abstract

The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N. This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial role must be played by the imaginary part of the effective action.