A practical solution to the sign problem in a matrix model for dynamical compactification

TL;DR

This paper introduces a practical method to overcome the sign problem in matrix models related to superstring theory, enabling more accurate Monte Carlo simulations of spontaneous symmetry breaking and space-time emergence.

Contribution

The authors generalize the factorization method to effectively address the sign problem in matrix models, validated through explicit Monte Carlo calculations and large-N extrapolations.

Findings

Confirmed spontaneous symmetry breaking due to fermion determinant phase

Reproduced previous results with the Gaussian expansion method

Clarified features of the approach applicable to other systems with sign problems

Abstract

The matrix model formulation of superstring theory offers the possibility to understand the appearance of 4d space-time from 10d as a consequence of spontaneous breaking of the SO(10) symmetry. Monte Carlo studies of this issue is technically difficult due to the so-called sign problem. We present a practical solution to this problem generalizing the factorization method proposed originally by two of the authors (K.N.A. and J.N.). Explicit Monte Carlo calculations and large-N extrapolations are performed in a simpler matrix model with similar properties, and reproduce quantitative results obtained previously by the Gaussian expansion method. Our results also confirm that the spontaneous symmetry breaking indeed occurs due to the phase of the fermion determinant, which vanishes for collapsed configurations. We clarify various generic features of this approach, which would be useful in applying it to other statistical systems with the sign problem.