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

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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.

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Authors and Affiliations

  1. Physics Department, National Technical University, Zografou Campus, GR-15780, Athens, Greece

    Konstantinos N. Anagnostopoulos

  2. Institute for Fundamental Sciences, Setsunan University, 17-8 Ikeda Nakamachi, Neyagawa, Osaka, 572-8508, Japan

    Takehiro Azuma

  3. KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Jun Nishimura

  4. Department of Particle and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan

    Jun Nishimura

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  1. Konstantinos N. Anagnostopoulos
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  2. Takehiro Azuma
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  3. Jun Nishimura
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Correspondence to Takehiro Azuma.

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ArXiv ePrint: 1108.1534

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Anagnostopoulos, K.N., Azuma, T. & Nishimura, J. A practical solution to the sign problem in a matrix model for dynamical compactification. J. High Energ. Phys. 2011, 126 (2011). https://doi.org/10.1007/JHEP10(2011)126

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