Monte Carlo studies of the IIB matrix model at large N
Monte Carlo studies of the IIB matrix model at large N
复制标题
大 N 时 IIB 矩阵模型的蒙特卡罗研究
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
T. Hotta
中科院分区：
文献类型：
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作者：
J. Ambjorn;J. Nishimura;K. Anagnostopoulos;W. Bietenholz;T. Hotta
H. Aoki等人提出的IIB矩阵模型的低能量有效理论仅用玻色子变量明确地表示出来。为了研究十维洛伦兹不变性自发击穿的可能性，对有效理论进行了蒙特卡罗模拟。有效动作的虚部，即在仿真中引起所谓符号问题的虚部，是用手去掉的。玻色子矩阵的特征值分布范围呈现幂律大n行为，与简单的支链聚合物预测相一致。然而，我们观察到，随着n的增加，特征值分布在十维时空中变得越来越各向同性。这表明，如果在IIB矩阵模型中确实发生了洛伦兹不变性的自发破坏，那么有效作用的虚部必须发挥关键作用。
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 ten-dimensional 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.