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

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.

44 pages, 64 figures, v2: some minor typos corrected

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Cited by in corpus (11)

• High density QCD on a Lefschetz thimble?
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
• Late time behaviors of the expanding universe in the IIB matrix model
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Progress in the numerical studies of the type IIB matrix model
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method
• Recent developments in the type IIB matrix model